WorldWideScience

Sample records for lengthy hexadecimal numbers

  1. Effects of Minimal versus Lengthy Delay between Simulated and In Vivo Instruction on Community Performance.

    Science.gov (United States)

    Nietupski, John; And Others

    1985-01-01

    No differential effects were revealed between minimal and relatively lengthy intervals in simulated and in vivo training of two students (8 and 13 years old) with severe handicaps. Performance in community fast food restaurants was measured. (CL)

  2. Effect of Lengthy Root Canal Therapy Sessions on Temporomandibular Joint and Masticatory Muscles

    Directory of Open Access Journals (Sweden)

    Safoora Sahebi

    2010-09-01

    Full Text Available Background and aims. Trauma is one of the major factors associated with temporomandibular joint disorders (TMD. These disorders result from macro-trauma or micro-trauma. Macro-trauma might be iatrogenic; for example, from intubation procedures, third molar extraction procedures, and lengthy dental appointments. The aim of this study was to evaluate the effect of lengthy root canal therapy (more than 2 hours on TMJ and its supporting structures. Materials and methods. Eighty patients whose root canal therapy session lasted more than 2 hours were examined for the status of TMJ and masticatory muscles. After one week the second part of the examination was carried out for TMJ problems and pain and tenderness levels of masticatory muscles. Data was analyzed using Wilcoxon statistical test. Results. Women showed more pain compared to men. There was a significant increase in pain in the external acoustic meatus examination one week after root canal therapy. Patients who were treated for their posterior teeth suffered more pain than those who were treated for the anteriors and premolars. Other aspects of the examination were not affected significantly by lengthy root canal therapy. Conclusion. Lengthy dental treatments can harm TMJ and masticatory muscles and wide opening of the mouth during such appointments can worsen the situation. Therefore, it is wise to break the appointment into shorter intervals and let the patients rest during treatment to close their mouth to prevent iatrogenic damage to TMJ.

  3. Effect of Lengthy Root Canal Therapy Sessions on Temporomandibular Joint and Masticatory Muscles

    Science.gov (United States)

    Sahebi, Safoora; Moazami, Fariborz; Afsa, Masoomeh; Nabavi Zade, Mohammad Reza

    2010-01-01

    Background and aims Trauma is one of the major factors associated with temporomandibular joint disorders (TMD). These disorders result from macro-trauma or micro-trauma. Macro-trauma might be iatrogenic; for example, from intuba-tion procedures, third molar extraction procedures, and lengthy dental appointments. The aim of this study was to evaluate the effect of lengthy root canal therapy (more than 2 hours) on TMJ and its supporting structures. Materials and methods Eighty patients whose root canal therapy session lasted more than 2 hours were examined for the status of TMJ and masticatory muscles. After one week the second part of the examination was carried out for TMJ problems and pain and tenderness levels of masticatory muscles. Data was analyzed using Wilcoxon statistical test. Results Women showed more pain compared to men. There was a significant increase in pain in the external acoustic meatus examination one week after root canal therapy. Patients who were treated for their posterior teeth suffered more pain than those who were treated for the anteriors and premolars. Other aspects of the examination were not affected significantly by lengthy root canal therapy. Conclusion Lengthy dental treatments can harm TMJ and masticatory muscles and wide opening of the mouth during such appointments can worsen the situation. Therefore, it is wise to break the appointment into shorter intervals and let the patients rest during treatment to close their mouth to prevent iatrogenic damage to TMJ. PMID:22991607

  4. Rapid progress or lengthy process? electronic personal health records in mental health

    Directory of Open Access Journals (Sweden)

    Denis Mike

    2011-07-01

    Full Text Available Abstract A major objective of many healthcare providers is to increase patients' participation in their own care. The introduction of electronic personal health records (ePHRs may help to achieve this. An ePHR is an electronic database of an individual's health information, accessible to and maintained by the patient. ePHRs are very much in vogue, with an increasing number of studies reporting their potential utility as well as cost. However, the vast majority of these studies focus on general healthcare. Little attempt has been made to document the specific problems which might occur throughout the implementation of ePHRs in mental health. This review identifies such concerns through an electronic search of the literature. Several potential difficulties are highlighted and addressed, including access to information technology, identifying relevant populations and the handling of sensitive information. Special attention is paid to the concept of 'empowerment' and what this means in relation to ePHRs.

  5. Pattern of pre-existing IgG subclass responses to a panel of asexual stage malaria antigens reported during the lengthy dry season in Daraweesh, Sudan

    DEFF Research Database (Denmark)

    Nasr, A; Iriemenam, N C; Troye-Blomberg, M

    2011-01-01

    The anti-malarial IgG immune response during the lengthy and dry season in areas of low malaria transmission as in Eastern Sudan is largely unknown. In this study, ELISA was used for the measurement of pre-existing total IgG and IgG subclasses to a panel of malaria antigens, MSP2-3D7, MSP2-FC27...

  6. NRC hopes to discourage lengthy onsite storage

    International Nuclear Information System (INIS)

    Anon.

    1993-01-01

    Now it has become clear why last year's partial voiding of the Low-Level Waste Policy Amendments Act was seen as significant in some quarters. On June 19, 1992, the US Supreme Court ruled that the passage requiring states to take title to LLW produced within their borders was unconstitutional (NN, July 1992, p. 17). This did not change the facts that LLW is still being generated, and that interstate compacts with licensed disposal sites are now empowered to refuse LLW from outside the compacts. Still, state officials had a reason to be relieved-because they knew that the Nuclear Regulatory Commission was at work on a regulation that would have made them take title to LLW, at a radwaste generator's request, at any time after January 1, 1996, if the state did not have access to a licensed disposal site. The court ruling has forced the NRC to take this passage out of the proposal, but the agency has still gone ahead and published draft amendments intended to establish long-term onsite storage as the last resort option for LLW management

  7. Sagan numbers

    OpenAIRE

    Mendonça, J. Ricardo G.

    2012-01-01

    We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by the North-american astronomer Carl E. Sagan in his science-fiction novel "Contact." Sagan numbers hold connections with a wealth of mathematical ideas. We describe some properties of the newly defined numbers and indicate directions for further amusement.

  8. Fibonacci numbers

    CERN Document Server

    Vorob'ev, Nikolai Nikolaevich

    2011-01-01

    Fibonacci numbers date back to an 800-year-old problem concerning the number of offspring born in a single year to a pair of rabbits. This book offers the solution and explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. A discussion of the ""golden section"" rectangle, in which the lengths of the sides can be expressed as a ration of two successive Fibonacci numbers, draws upon attempts by ancient and medieval thinkers to base aesthetic and philosophical principles on the beauty of these figures. Recreational readers as well as students and teacher

  9. Number names and number understanding

    DEFF Research Database (Denmark)

    Ejersbo, Lisser Rye; Misfeldt, Morten

    2014-01-01

    through using mathematical names for the numbers such as one-ten-one for 11 and five-ten-six for 56. The project combines the renaming of numbers with supporting the teaching with the new number names. Our hypothesis is that Danish children have more difficulties learning and working with numbers, because...... the Danish number names are more complicated than in other languages. Keywords: A research project in grade 0 and 1th in a Danish school, Base-10 system, two-digit number names, semiotic, cognitive perspectives....

  10. Eulerian numbers

    CERN Document Server

    Petersen, T Kyle

    2015-01-01

    This text presents the Eulerian numbers in the context of modern enumerative, algebraic, and geometric combinatorics. The book first studies Eulerian numbers from a purely combinatorial point of view, then embarks on a tour of how these numbers arise in the study of hyperplane arrangements, polytopes, and simplicial complexes. Some topics include a thorough discussion of gamma-nonnegativity and real-rootedness for Eulerian polynomials, as well as the weak order and the shard intersection order of the symmetric group. The book also includes a parallel story of Catalan combinatorics, wherein the Eulerian numbers are replaced with Narayana numbers. Again there is a progression from combinatorics to geometry, including discussion of the associahedron and the lattice of noncrossing partitions. The final chapters discuss how both the Eulerian and Narayana numbers have analogues in any finite Coxeter group, with many of the same enumerative and geometric properties. There are four supplemental chapters throughout, ...

  11. Transfinite Numbers

    Indian Academy of Sciences (India)

    Transfinite Numbers. What is Infinity? S M Srivastava. In a series of revolutionary articles written during the last quarter of the nineteenth century, the great Ger- man mathematician Georg Cantor removed the age-old mistrust of infinity and created an exceptionally beau- tiful and useful theory of transfinite numbers. This is.

  12. Number theory

    CERN Document Server

    Andrews, George E

    1994-01-01

    Although mathematics majors are usually conversant with number theory by the time they have completed a course in abstract algebra, other undergraduates, especially those in education and the liberal arts, often need a more basic introduction to the topic.In this book the author solves the problem of maintaining the interest of students at both levels by offering a combinatorial approach to elementary number theory. In studying number theory from such a perspective, mathematics majors are spared repetition and provided with new insights, while other students benefit from the consequent simpl

  13. Nice numbers

    CERN Document Server

    Barnes, John

    2016-01-01

    In this intriguing book, John Barnes takes us on a journey through aspects of numbers much as he took us on a geometrical journey in Gems of Geometry. Similarly originating from a series of lectures for adult students at Reading and Oxford University, this book touches a variety of amusing and fascinating topics regarding numbers and their uses both ancient and modern. The author intrigues and challenges his audience with both fundamental number topics such as prime numbers and cryptography, and themes of daily needs and pleasures such as counting one's assets, keeping track of time, and enjoying music. Puzzles and exercises at the end of each lecture offer additional inspiration, and numerous illustrations accompany the reader. Furthermore, a number of appendices provides in-depth insights into diverse topics such as Pascal’s triangle, the Rubik cube, Mersenne’s curious keyboards, and many others. A theme running through is the thought of what is our favourite number. Written in an engaging and witty sty...

  14. Number names and number understanding

    DEFF Research Database (Denmark)

    Ejersbo, Lisser Rye; Misfeldt, Morten

    2014-01-01

    This paper concerns the results from the first year of a three-year research project involving the relationship between Danish number names and their corresponding digits in the canonical base 10 system. The project aims to develop a system to help the students’ understanding of the base 10 system...... the Danish number names are more complicated than in other languages. Keywords: A research project in grade 0 and 1th in a Danish school, Base-10 system, two-digit number names, semiotic, cognitive perspectives....

  15. Funny Numbers

    Directory of Open Access Journals (Sweden)

    Theodore M. Porter

    2012-12-01

    Full Text Available The struggle over cure rate measures in nineteenth-century asylums provides an exemplary instance of how, when used for official assessments of institutions, these numbers become sites of contestation. The evasion of goals and corruption of measures tends to make these numbers “funny” in the sense of becoming dis-honest, while the mismatch between boring, technical appearances and cunning backstage manipulations supplies dark humor. The dangers are evident in recent efforts to decentralize the functions of governments and corporations using incen-tives based on quantified targets.

  16. Number Guessing

    Science.gov (United States)

    Sezin, Fatin

    2009-01-01

    It is instructive and interesting to find hidden numbers by using different positional numeration systems. Most of the present guessing techniques use the binary system expressed as less-than, greater-than or present-absent type information. This article describes how, by employing four cards having integers 1-64 written in different colours, one…

  17. Transfinite Numbers

    Indian Academy of Sciences (India)

    this is a characteristic difference between finite and infinite sets and created an immensely useful branch of mathematics based on this idea which had a great impact on the whole of mathe- matics. For example, the question of what is a number (finite or infinite) is almost a philosophical one. However Cantor's work turned it ...

  18. Transfinite Numbers

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 3. Transfinite Numbers - What is Infinity? S M Srivastava. General Article Volume 2 Issue 3 March 1997 pp 58-68. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/002/03/0058-0068 ...

  19. Number Sense on the Number Line

    Science.gov (United States)

    Woods, Dawn Marie; Ketterlin Geller, Leanne; Basaraba, Deni

    2018-01-01

    A strong foundation in early number concepts is critical for students' future success in mathematics. Research suggests that visual representations, like a number line, support students' development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction…

  20. On the number of special numbers

    Indian Academy of Sciences (India)

    ... factorizaton for all exponents. Let V ( x ) be the number of special numbers ≤ x . We will prove that there is a constant c > 1 such that V ( x ) ∼ c x l o g x . We will make some remarks on determining the error term at the end. Using the explicit abc conjecture, we will study the existence of 23 consecutive special integers.

  1. Number words and number symbols a cultural history of numbers

    CERN Document Server

    Menninger, Karl

    1992-01-01

    Classic study discusses number sequence and language and explores written numerals and computations in many cultures. "The historian of mathematics will find much to interest him here both in the contents and viewpoint, while the casual reader is likely to be intrigued by the author's superior narrative ability.

  2. Those fascinating numbers

    CERN Document Server

    Koninck, Jean-Marie De

    2009-01-01

    Who would have thought that listing the positive integers along with their most remarkable properties could end up being such an engaging and stimulating adventure? The author uses this approach to explore elementary and advanced topics in classical number theory. A large variety of numbers are contemplated: Fermat numbers, Mersenne primes, powerful numbers, sublime numbers, Wieferich primes, insolite numbers, Sastry numbers, voracious numbers, to name only a few. The author also presents short proofs of miscellaneous results and constantly challenges the reader with a variety of old and new n

  3. Introduction to number theory

    CERN Document Server

    Vazzana, Anthony; Garth, David

    2007-01-01

    One of the oldest branches of mathematics, number theory is a vast field devoted to studying the properties of whole numbers. Offering a flexible format for a one- or two-semester course, Introduction to Number Theory uses worked examples, numerous exercises, and two popular software packages to describe a diverse array of number theory topics.

  4. Building Numbers from Primes

    Science.gov (United States)

    Burkhart, Jerry

    2009-01-01

    Prime numbers are often described as the "building blocks" of natural numbers. This article shows how the author and his students took this idea literally by using prime factorizations to build numbers with blocks. In this activity, students explore many concepts of number theory, including the relationship between greatest common factors and…

  5. Consistent linguistic fuzzy preference relations method with ranking fuzzy numbers

    Science.gov (United States)

    Ridzuan, Siti Amnah Mohd; Mohamad, Daud; Kamis, Nor Hanimah

    2014-12-01

    Multi-Criteria Decision Making (MCDM) methods have been developed to help decision makers in selecting the best criteria or alternatives from the options given. One of the well known methods in MCDM is the Consistent Fuzzy Preference Relation (CFPR) method, essentially utilizes a pairwise comparison approach. This method was later improved to cater subjectivity in the data by using fuzzy set, known as the Consistent Linguistic Fuzzy Preference Relations (CLFPR). The CLFPR method uses the additive transitivity property in the evaluation of pairwise comparison matrices. However, the calculation involved is lengthy and cumbersome. To overcome this problem, a method of defuzzification was introduced by researchers. Nevertheless, the defuzzification process has a major setback where some information may lose due to the simplification process. In this paper, we propose a method of CLFPR that preserves the fuzzy numbers form throughout the process. In obtaining the desired ordering result, a method of ranking fuzzy numbers is utilized in the procedure. This improved procedure for CLFPR is implemented to a case study to verify its effectiveness. This method is useful for solving decision making problems and can be applied to many areas of applications.

  6. Algebraic number theory

    CERN Document Server

    Jarvis, Frazer

    2014-01-01

    The technical difficulties of algebraic number theory often make this subject appear difficult to beginners. This undergraduate textbook provides a welcome solution to these problems as it provides an approachable and thorough introduction to the topic. Algebraic Number Theory takes the reader from unique factorisation in the integers through to the modern-day number field sieve. The first few chapters consider the importance of arithmetic in fields larger than the rational numbers. Whilst some results generalise well, the unique factorisation of the integers in these more general number fields often fail. Algebraic number theory aims to overcome this problem. Most examples are taken from quadratic fields, for which calculations are easy to perform. The middle section considers more general theory and results for number fields, and the book concludes with some topics which are more likely to be suitable for advanced students, namely, the analytic class number formula and the number field sieve. This is the fi...

  7. p-adic numbers

    OpenAIRE

    Grešak, Rozalija

    2015-01-01

    The field of real numbers is usually constructed using Dedekind cuts. In these thesis we focus on the construction of the field of real numbers using metric completion of rational numbers using Cauchy sequences. In a similar manner we construct the field of p-adic numbers, describe some of their basic and topological properties. We follow by a construction of complex p-adic numbers and we compare them with the ordinary complex numbers. We conclude the thesis by giving a motivation for the int...

  8. On the number of special numbers

    Indian Academy of Sciences (India)

    We now apply the theory of the Thue equation to obtain an effective bound on m. Indeed, by Lemma 3.2, we can write m2 = ba3 and m2 − 4 = cd3 with b, c cubefree. By the above, both b, c are bounded since they are cubefree and all their prime factors are less than e63727. Now we have a finite number of. Thue equations:.

  9. Hawaiian Number Systems.

    Science.gov (United States)

    Hughes, Barnabas

    1982-01-01

    The history of Hawaiian number systems is examined, and answers to questions regarding Hawaiian number words, including their origin and factors that influenced their development, are covered. A brief guide for pronouncing Hawaiian words is also provided. (MP)

  10. Making decisions from numbers

    Energy Technology Data Exchange (ETDEWEB)

    Somers, E.

    1987-03-01

    Regulatory agencies require numbers to provide health protection. The manner in which these numbers are derived from animal experiments and human epidemiology is considered together with the limitations and inadequacies of these numbers. Some recent examples of risk assessment in Canada are given including asbestos, drinking water, and indoor air quality. The value of these numbers in providing a measure of the hazard in a wider perspective is stressed, although they can never be the sole determinant of public policy.

  11. Analytic number theory

    CERN Document Server

    Matsumoto, Kohji

    2002-01-01

    The book includes several survey articles on prime numbers, divisor problems, and Diophantine equations, as well as research papers on various aspects of analytic number theory such as additive problems, Diophantine approximations and the theory of zeta and L-function Audience Researchers and graduate students interested in recent development of number theory

  12. Safety-in-numbers

    DEFF Research Database (Denmark)

    Elvik, Rune; Bjørnskau, Torkel

    2017-01-01

    Highlights •26 studies of the safety-in-numbers effect are reviewed. •The existence of a safety-in-numbers effect is confirmed. •Results are consistent. •Causes of the safety-in-numbers effect are incompletely known....

  13. Asymptotic numbers: Pt.1

    International Nuclear Information System (INIS)

    Todorov, T.D.

    1980-01-01

    The set of asymptotic numbers A as a system of generalized numbers including the system of real numbers R, as well as infinitely small (infinitesimals) and infinitely large numbers, is introduced. The detailed algebraic properties of A, which are unusual as compared with the known algebraic structures, are studied. It is proved that the set of asymptotic numbers A cannot be isomorphically embedded as a subspace in any group, ring or field, but some particular subsets of asymptotic numbers are shown to be groups, rings, and fields. The algebraic operation, additive and multiplicative forms, and the algebraic properties are constructed in an appropriate way. It is shown that the asymptotic numbers give rise to a new type of generalized functions quite analogous to the distributions of Schwartz allowing, however, the operation multiplication. A possible application of these functions to quantum theory is discussed

  14. Applied number theory

    CERN Document Server

    Niederreiter, Harald

    2015-01-01

    This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas.  Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc.  Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters...

  15. Invitation to number theory

    CERN Document Server

    Ore, Oystein

    2017-01-01

    Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.

  16. Predicting Lotto Numbers

    DEFF Research Database (Denmark)

    Jørgensen, Claus Bjørn; Suetens, Sigrid; Tyran, Jean-Robert

    numbers based on recent drawings. While most players pick the same set of numbers week after week without regards of numbers drawn or anything else, we find that those who do change, act on average in the way predicted by the law of small numbers as formalized in recent behavioral theory. In particular......We investigate the “law of small numbers” using a unique panel data set on lotto gambling. Because we can track individual players over time, we can measure how they react to outcomes of recent lotto drawings. We can therefore test whether they behave as if they believe they can predict lotto......, on average they move away from numbers that have recently been drawn, as suggested by the “gambler’s fallacy”, and move toward numbers that are on streak, i.e. have been drawn several weeks in a row, consistent with the “hot hand fallacy”....

  17. The simple complex numbers

    OpenAIRE

    Zalesny, Jaroslaw

    2008-01-01

    A new simple geometrical interpretation of complex numbers is presented. It differs from their usual interpretation as points in the complex plane. From the new point of view the complex numbers are rather operations on vectors than points. Moreover, in this approach the real, imaginary and complex numbers have similar interpretation. They are simply some operations on vectors. The presented interpretation is simpler, more natural, and better adjusted to possible applications in geometry and ...

  18. Predicting Lotto Numbers

    DEFF Research Database (Denmark)

    Suetens, Sigrid; Galbo-Jørgensen, Claus B.; Tyran, Jean-Robert Karl

    2016-01-01

    as formalized in recent behavioral theory. In particular, players tend to bet less on numbers that have been drawn in the preceding week, as suggested by the ‘gambler’s fallacy’, and bet more on a number if it was frequently drawn in the recent past, consistent with the ‘hot-hand fallacy’.......We investigate the ‘law of small numbers’ using a data set on lotto gambling that allows us to measure players’ reactions to draws. While most players pick the same set of numbers week after week, we find that those who do change react on average as predicted by the law of small numbers...

  19. Intuitive numbers guide decisions

    Directory of Open Access Journals (Sweden)

    Ellen Peters

    2008-12-01

    Full Text Available Measuring reaction times to number comparisons is thought to reveal a processing stage in elementary numerical cognition linked to internal, imprecise representations of number magnitudes. These intuitive representations of the mental number line have been demonstrated across species and human development but have been little explored in decision making. This paper develops and tests hypotheses about the influence of such evolutionarily ancient, intuitive numbers on human decisions. We demonstrate that individuals with more precise mental-number-line representations are higher in numeracy (number skills consistent with previous research with children. Individuals with more precise representations (compared to those with less precise representations also were more likely to choose larger, later amounts over smaller, immediate amounts, particularly with a larger proportional difference between the two monetary outcomes. In addition, they were more likely to choose an option with a larger proportional but smaller absolute difference compared to those with less precise representations. These results are consistent with intuitive number representations underlying: a perceived differences between numbers, b the extent to which proportional differences are weighed in decisions, and, ultimately, c the valuation of decision options. Human decision processes involving numbers important to health and financial matters may be rooted in elementary, biological processes shared with other species.

  20. Beurling generalized numbers

    CERN Document Server

    Diamond, Harold G; Cheung, Man Ping

    2016-01-01

    "Generalized numbers" is a multiplicative structure introduced by A. Beurling to study how independent prime number theory is from the additivity of the natural numbers. The results and techniques of this theory apply to other systems having the character of prime numbers and integers; for example, it is used in the study of the prime number theorem (PNT) for ideals of algebraic number fields. Using both analytic and elementary methods, this book presents many old and new theorems, including several of the authors' results, and many examples of extremal behavior of g-number systems. Also, the authors give detailed accounts of the L^2 PNT theorem of J. P. Kahane and of the example created with H. L. Montgomery, showing that additive structure is needed for proving the Riemann hypothesis. Other interesting topics discussed are propositions "equivalent" to the PNT, the role of multiplicative convolution and Chebyshev's prime number formula for g-numbers, and how Beurling theory provides an interpretation of the ...

  1. Numbers, sequences and series

    CERN Document Server

    Hirst, Keith

    1994-01-01

    Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite proc

  2. The adventure of numbers

    CERN Document Server

    Godefroy, Gilles

    2004-01-01

    Numbers are fascinating. The fascination begins in childhood, when we first learn to count. It continues as we learn arithmetic, algebra, geometry, and so on. Eventually, we learn that numbers not only help us to measure the world, but also to understand it and, to some extent, to control it. In The Adventure of Numbers, Gilles Godefroy follows the thread of our expanding understanding of numbers to lead us through the history of mathematics. His goal is to share the joy of discovering and understanding this great adventure of the mind. The development of mathematics has been punctuated by a n

  3. The Class Number Problem

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 3; Issue 7. The Class Number Problem - An Introduction to Algebraic Number Theory. Rajat Tandon. General ... Author Affiliations. Rajat Tandon1. Department of Mathematics, University of Hyderabad, Central University P.O., Hyderabad 500 046, India ...

  4. The Class Number Problem

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 3; Issue 7. The Class Number Problem - An Introduction to Algebraic Number Theory. Rajat Tandon. General Article Volume 3 Issue 7 July 1998 pp 28-37. Fulltext. Click here to view fulltext PDF. Permanent link:

  5. The Class Number Problem

    Indian Academy of Sciences (India)

    The Class Number Problem. 2. An Introduction to Algebraic Number Theory. Rajat Tandon received his PhD from Yale. University, USA. After an initial period as a visiting post-doctoral fellow at. TIFR, he joined the faculty of the North. Eastern Hill University, where he taught for a few years. For about two decades now, he ...

  6. A Numbers Game

    DEFF Research Database (Denmark)

    Levin, Bruce R; McCall, Ingrid C.; Perrot, Veronique

    2017-01-01

    We postulate that the inhibition of growth and low rates of mortality of bacteria exposed to ribosome-binding antibiotics deemed bacteriostatic can be attributed almost uniquely to these drugs reducing the number of ribosomes contributing to protein synthesis, i.e., the number of effective riboso...

  7. The Congruent Number Problem

    Indian Academy of Sciences (India)

    Given a positive integer n, is there a simple criterion which enables us to decide whether or not n is congruent? A few remarks are in order. To start with, if we ..... In other words 1 is a congruent number. Combining Propositions 2 and 3 with the fact that 1 is a non-congruent number, we deduce Fermat's last theorem for n=4.

  8. Templates, Numbers & Watercolors.

    Science.gov (United States)

    Clemesha, David J.

    1990-01-01

    Describes how a second-grade class used large templates to draw and paint five-digit numbers. The lesson integrated artistic knowledge and vocabulary with their mathematics lesson in place value. Students learned how draftspeople use templates, and they studied number paintings by Charles Demuth and Jasper Johns. (KM)

  9. Elementary number theory

    CERN Document Server

    Dudley, Underwood

    2008-01-01

    Ideal for a first course in number theory, this lively, engaging text requires only a familiarity with elementary algebra and the properties of real numbers. Author Underwood Dudley, who has written a series of popular mathematics books, maintains that the best way to learn mathematics is by solving problems. In keeping with this philosophy, the text includes nearly 1,000 exercises and problems-some computational and some classical, many original, and some with complete solutions. The opening chapters offer sound explanations of the basics of elementary number theory and develop the fundamenta

  10. Numbers and computers

    CERN Document Server

    Kneusel, Ronald T

    2015-01-01

    This is a book about numbers and how those numbers are represented in and operated on by computers. It is crucial that developers understand this area because the numerical operations allowed by computers, and the limitations of those operations, especially in the area of floating point math, affect virtually everything people try to do with computers. This book aims to fill this gap by exploring, in sufficient but not overwhelming detail, just what it is that computers do with numbers. Divided into two parts, the first deals with standard representations of integers and floating point numb

  11. On powerful numbers

    Directory of Open Access Journals (Sweden)

    R. A. Mollin

    1986-01-01

    Full Text Available A powerful number is a positive integer n satisfying the property that p2 divides n whenever the prime p divides n; i.e., in the canonical prime decomposition of n, no prime appears with exponent 1. In [1], S.W. Golomb introduced and studied such numbers. In particular, he asked whether (25,27 is the only pair of consecutive odd powerful numbers. This question was settled in [2] by W.A. Sentance who gave necessary and sufficient conditions for the existence of such pairs. The first result of this paper is to provide a generalization of Sentance's result by giving necessary and sufficient conditions for the existence of pairs of powerful numbers spaced evenly apart. This result leads us naturally to consider integers which are representable as a proper difference of two powerful numbers, i.e. n=p1−p2 where p1 and p2 are powerful numbers with g.c.d. (p1,p2=1. Golomb (op.cit. conjectured that 6 is not a proper difference of two powerful numbers, and that there are infinitely many numbers which cannot be represented as a proper difference of two powerful numbers. The antithesis of this conjecture was proved by W.L. McDaniel [3] who verified that every non-zero integer is in fact a proper difference of two powerful numbers in infinitely many ways. McDaniel's proof is essentially an existence proof. The second result of this paper is a simpler proof of McDaniel's result as well as an effective algorithm (in the proof for explicitly determining infinitely many such representations. However, in both our proof and McDaniel's proof one of the powerful numbers is almost always a perfect square (namely one is always a perfect square when n≢2(mod4. We provide in §2 a proof that all even integers are representable in infinitely many ways as a proper nonsquare difference; i.e., proper difference of two powerful numbers neither of which is a perfect square. This, in conjunction with the odd case in [4], shows that every integer is representable in

  12. Algebraic number theory

    CERN Document Server

    Weiss, Edwin

    1998-01-01

    Careful organization and clear, detailed proofs characterize this methodical, self-contained exposition of basic results of classical algebraic number theory from a relatively modem point of view. This volume presents most of the number-theoretic prerequisites for a study of either class field theory (as formulated by Artin and Tate) or the contemporary treatment of analytical questions (as found, for example, in Tate's thesis).Although concerned exclusively with algebraic number fields, this treatment features axiomatic formulations with a considerable range of applications. Modem abstract te

  13. Brief history of numbers

    CERN Document Server

    Corry, Leo

    2015-01-01

    The world around us is saturated with numbers. They are a fundamental pillar of our modern society, and accepted and used with hardly a second thought. But how did this state of affairs come to be? In this book, Leo Corry tells the story behind the idea of number from the early days of the Pythagoreans, up until the turn of the twentieth century. He presents an overview of how numbers were handled and conceived in classical Greek mathematics, in the mathematics of Islam, in European mathematics of the middle ages and the Renaissance, during the scientific revolution, all the way through to the

  14. Fundamentals of number theory

    CERN Document Server

    LeVeque, William J

    1996-01-01

    This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given - making the book self-contained in this respect.The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diopha

  15. Advanced number theory

    CERN Document Server

    Cohn, Harvey

    1980-01-01

    ""A very stimulating book ... in a class by itself."" - American Mathematical MonthlyAdvanced students, mathematicians and number theorists will welcome this stimulating treatment of advanced number theory, which approaches the complex topic of algebraic number theory from a historical standpoint, taking pains to show the reader how concepts, definitions and theories have evolved during the last two centuries. Moreover, the book abounds with numerical examples and more concrete, specific theorems than are found in most contemporary treatments of the subject.The book is divided into three parts

  16. Professor Stewart's incredible numbers

    CERN Document Server

    Stewart, Ian

    2015-01-01

    Ian Stewart explores the astonishing properties of numbers from 1 to10 to zero and infinity, including one figure that, if you wrote it out, would span the universe. He looks at every kind of number you can think of - real, imaginary, rational, irrational, positive and negative - along with several you might have thought you couldn't think of. He explains the insights of the ancient mathematicians, shows how numbers have evolved through the ages, and reveals the way numerical theory enables everyday life. Under Professor Stewart's guidance you will discover the mathematics of codes,

  17. Random number generation

    International Nuclear Information System (INIS)

    Coveyou, R.R.

    1974-01-01

    The subject of random number generation is currently controversial. Differing opinions on this subject seem to stem from implicit or explicit differences in philosophy; in particular, from differing ideas concerning the role of probability in the real world of physical processes, electronic computers, and Monte Carlo calculations. An attempt is made here to reconcile these views. The role of stochastic ideas in mathematical models is discussed. In illustration of these ideas, a mathematical model of the use of random number generators in Monte Carlo calculations is constructed. This model is used to set up criteria for the comparison and evaluation of random number generators. (U.S.)

  18. The emergence of number

    CERN Document Server

    Crossley, John N

    1987-01-01

    This book presents detailed studies of the development of three kinds of number. In the first part the development of the natural numbers from Stone-Age times right up to the present day is examined not only from the point of view of pure history but also taking into account archaeological, anthropological and linguistic evidence. The dramatic change caused by the introduction of logical theories of number in the 19th century is also treated and this part ends with a non-technical account of the very latest developments in the area of Gödel's theorem. The second part is concerned with the deve

  19. Supersymmetric Displaced Number States

    Directory of Open Access Journals (Sweden)

    Fredy R. Zypman

    2015-06-01

    Full Text Available We introduce, generate and study a family of supersymmetric displaced number states (SDNS that can be considered generalized coherent states of the supersymmetric harmonic oscillator. The family is created from the seminal supersymmetric boson-fermion entangling annihilation operator introduced by Aragone and Zypman and later expanded by Kornbluth and Zypman. Using the momentum representation, the states are obtained analytically in compact form as displaced supersymmetric number states. We study their position-momentum uncertainties, and their bunchiness by classifying them according to their Mandel Q-parameter in phase space. We were also able to find closed form analytical representations in the space and number basis.

  20. High Reynolds Number Turbulence

    National Research Council Canada - National Science Library

    Smits, Alexander J

    2007-01-01

    The objectives of the grant were to provide a systematic study to fill the gap between existing research on low Reynolds number turbulent flows to the kinds of turbulent flows encountered on full-scale vehicles...

  1. Really big numbers

    CERN Document Server

    Schwartz, Richard Evan

    2014-01-01

    In the American Mathematical Society's first-ever book for kids (and kids at heart), mathematician and author Richard Evan Schwartz leads math lovers of all ages on an innovative and strikingly illustrated journey through the infinite number system. By means of engaging, imaginative visuals and endearing narration, Schwartz manages the monumental task of presenting the complex concept of Big Numbers in fresh and relatable ways. The book begins with small, easily observable numbers before building up to truly gigantic ones, like a nonillion, a tredecillion, a googol, and even ones too huge for names! Any person, regardless of age, can benefit from reading this book. Readers will find themselves returning to its pages for a very long time, perpetually learning from and growing with the narrative as their knowledge deepens. Really Big Numbers is a wonderful enrichment for any math education program and is enthusiastically recommended to every teacher, parent and grandparent, student, child, or other individual i...

  2. Solar Indices - Sunspot Numbers

    Data.gov (United States)

    National Oceanic and Atmospheric Administration, Department of Commerce — Collection includes a variety of indices related to solar activity contributed by a number of national and private solar observatories located worldwide. This...

  3. Volume 9 Number 2

    African Journals Online (AJOL)

    OLUWOLE

    Table 1: Insect Invaders Encountered and their Stages at Collection from Decaying. Banana / Plantain Pseudo stems. Insect Order. Family. Genus. Species. Life Stage Encountered. Number (%). Coleoptera. Curculionidae Curculionidae. Curculionidae Curculionidae. Curculionidae Curculionidae. Curculionidae.

  4. Quantum random number generator

    Science.gov (United States)

    Pooser, Raphael C.

    2016-05-10

    A quantum random number generator (QRNG) and a photon generator for a QRNG are provided. The photon generator may be operated in a spontaneous mode below a lasing threshold to emit photons. Photons emitted from the photon generator may have at least one random characteristic, which may be monitored by the QRNG to generate a random number. In one embodiment, the photon generator may include a photon emitter and an amplifier coupled to the photon emitter. The amplifier may enable the photon generator to be used in the QRNG without introducing significant bias in the random number and may enable multiplexing of multiple random numbers. The amplifier may also desensitize the photon generator to fluctuations in power supplied thereto while operating in the spontaneous mode. In one embodiment, the photon emitter and amplifier may be a tapered diode amplifier.

  5. Drawing a random number

    DEFF Research Database (Denmark)

    Wanscher, Jørgen Bundgaard; Sørensen, Majken Vildrik

    2006-01-01

    Random numbers are used for a great variety of applications in almost any field of computer and economic sciences today. Examples ranges from stock market forecasting in economics, through stochastic traffic modelling in operations research to photon and ray tracing in graphics. The construction...... of a model or a solution method requires certain characteristics of the random numbers used. This is usually a distribution classification, which the sequence of random numbers must fulfill; of these some are very hard to fulfill and others are next to impossible. Today mathematics allows us to transform...... highly uniform multidimensional draws, which are highly relevant for todays traffic models. This paper shows among others combined shuffling and scrambling seems needless, that scrambling gives the lowest correlation and that there are detectable differences between random numbers, dependent...

  6. Report number codes

    International Nuclear Information System (INIS)

    Nelson, R.N.

    1985-05-01

    This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name

  7. Report number codes

    Energy Technology Data Exchange (ETDEWEB)

    Nelson, R.N. (ed.)

    1985-05-01

    This publication lists all report number codes processed by the Office of Scientific and Technical Information. The report codes are substantially based on the American National Standards Institute, Standard Technical Report Number (STRN)-Format and Creation Z39.23-1983. The Standard Technical Report Number (STRN) provides one of the primary methods of identifying a specific technical report. The STRN consists of two parts: The report code and the sequential number. The report code identifies the issuing organization, a specific program, or a type of document. The sequential number, which is assigned in sequence by each report issuing entity, is not included in this publication. Part I of this compilation is alphabetized by report codes followed by issuing installations. Part II lists the issuing organization followed by the assigned report code(s). In both Parts I and II, the names of issuing organizations appear for the most part in the form used at the time the reports were issued. However, for some of the more prolific installations which have had name changes, all entries have been merged under the current name.

  8. The LHC in numbers

    CERN Multimedia

    Alizée Dauvergne

    2010-01-01

    What makes the LHC the biggest particle accelerator in the world? Here are some of the numbers that characterise the LHC, and their equivalents in terms that are easier for us to imagine.   Feature Number Equivalent Circumference ~ 27 km   Distance covered by beam in 10 hours ~ 10 billion km a round trip to Neptune Number of times a single proton travels around the ring each second 11 245   Speed of protons first entering the LHC 299 732 500 m/s 99.9998 % of the speed of light Speed of protons when they collide 299 789 760 m/s 99.9999991 % of the speed of light Collision temperature ~ 1016 °C ove...

  9. Chromosome numbers in Bromeliaceae

    Directory of Open Access Journals (Sweden)

    Cotias-de-Oliveira Ana Lúcia Pires

    2000-01-01

    Full Text Available The present study reports chromosome numbers of 17 species of Bromeliaceae, belonging to the genera Encholirium, Bromelia, Orthophytum, Hohenbergia, Billbergia, Neoglaziovia, Aechmea, Cryptanthus and Ananas. Most species present 2n = 50, however, Bromelia laciniosa, Orthophytum burle-marxii and O. maracasense are polyploids with 2n = 150, 2n = 100 and 2n = 150, respectively, while for Cryptanthus bahianus, 2n = 34 + 1-4B. B chromosomes were observed in Bromelia plumieri and Hohenbergia aff. utriculosa. The chromosome number of all species was determined for the first time, except for Billbergia chlorosticta and Cryptanthus bahianus. Our data supports the hypothesis of a basic number of x = 25 for the Bromeliaceae family and decreasing aneuploidy in the genus Cryptanthus.

  10. Quantum random number generator

    Science.gov (United States)

    Soubusta, Jan; Haderka, Ondrej; Hendrych, Martin

    2001-03-01

    Since reflection or transmission of a quantum particle on a beamsplitter is inherently random quantum process, a device built on this principle does not suffer from drawbacks of neither pseudo-random computer generators or classical noise sources. Nevertheless, a number of physical conditions necessary for high quality random numbers generation must be satisfied. Luckily, in quantum optics realization they can be well controlled. We present an easy random number generator based on the division of weak light pulses on a beamsplitter. The randomness of the generated bit stream is supported by passing the data through series of 15 statistical test. The device generates at a rate of 109.7 kbit/s.

  11. CONFUSION WITH TELEPHONE NUMBERS

    CERN Multimedia

    Telecom Service

    2002-01-01

    The area code is now required for all telephone calls within Switzerland. Unfortunately this is causing some confusion. CERN has received complaints that incoming calls intended for CERN mobile phones are being directed to private subscribers. This is caused by mistakenly dialing the WRONG code (e.g. 022) in front of the mobile number. In order to avoid these problems, please inform your correspondents that the correct numbers are: 079 201 XXXX from Switzerland; 0041 79 201 XXXX from other countries. Telecom Service  

  12. CONFUSION WITH TELEPHONE NUMBERS

    CERN Multimedia

    Telecom Service

    2002-01-01

    he area code is now required for all telephone calls within Switzerland. Unfortunately this is causing some confusion. CERN has received complaints that incoming calls intended for CERN mobile phones are being directed to private subscribers. This is caused by mistakenly dialing the WRONG code (e.g. 022) in front of the mobile number. In order to avoid these problems, please inform your correspondents that the correct numbers are: 079 201 XXXX from Switzerland; 0041 79 201 XXXX from other countries. Telecom Service

  13. Analytic number theory

    CERN Document Server

    Iwaniec, Henryk

    2004-01-01

    Analytic Number Theory distinguishes itself by the variety of tools it uses to establish results, many of which belong to the mainstream of arithmetic. One of the main attractions of analytic number theory is the vast diversity of concepts and methods it includes. The main goal of the book is to show the scope of the theory, both in classical and modern directions, and to exhibit its wealth and prospects, its beautiful theorems and powerful techniques. The book is written with graduate students in mind, and the authors tried to balance between clarity, completeness, and generality. The exercis

  14. Geometry of numbers

    CERN Document Server

    Gruber, Peter M

    1987-01-01

    This volume contains a fairly complete picture of the geometry of numbers, including relations to other branches of mathematics such as analytic number theory, diophantine approximation, coding and numerical analysis. It deals with convex or non-convex bodies and lattices in euclidean space, etc.This second edition was prepared jointly by P.M. Gruber and the author of the first edition. The authors have retained the existing text (with minor corrections) while adding to each chapter supplementary sections on the more recent developments. While this method may have drawbacks, it has the definit

  15. Algebraic theory of numbers

    CERN Document Server

    Samuel, Pierre

    2008-01-01

    Algebraic number theory introduces students not only to new algebraic notions but also to related concepts: groups, rings, fields, ideals, quotient rings and quotient fields, homomorphisms and isomorphisms, modules, and vector spaces. Author Pierre Samuel notes that students benefit from their studies of algebraic number theory by encountering many concepts fundamental to other branches of mathematics - algebraic geometry, in particular.This book assumes a knowledge of basic algebra but supplements its teachings with brief, clear explanations of integrality, algebraic extensions of fields, Gal

  16. Earthquake number forecasts testing

    Science.gov (United States)

    Kagan, Yan Y.

    2017-10-01

    We study the distributions of earthquake numbers in two global earthquake catalogues: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. The properties of these distributions are especially required to develop the number test for our forecasts of future seismic activity rate, tested by the Collaboratory for Study of Earthquake Predictability (CSEP). A common assumption, as used in the CSEP tests, is that the numbers are described by the Poisson distribution. It is clear, however, that the Poisson assumption for the earthquake number distribution is incorrect, especially for the catalogues with a lower magnitude threshold. In contrast to the one-parameter Poisson distribution so widely used to describe earthquake occurrences, the negative-binomial distribution (NBD) has two parameters. The second parameter can be used to characterize the clustering or overdispersion of a process. We also introduce and study a more complex three-parameter beta negative-binomial distribution. We investigate the dependence of parameters for both Poisson and NBD distributions on the catalogue magnitude threshold and on temporal subdivision of catalogue duration. First, we study whether the Poisson law can be statistically rejected for various catalogue subdivisions. We find that for most cases of interest, the Poisson distribution can be shown to be rejected statistically at a high significance level in favour of the NBD. Thereafter, we investigate whether these distributions fit the observed distributions of seismicity. For this purpose, we study upper statistical moments of earthquake numbers (skewness and kurtosis) and compare them to the theoretical values for both distributions. Empirical values for the skewness and the kurtosis increase for the smaller magnitude threshold and increase with even greater intensity for small temporal subdivision of catalogues. The Poisson distribution for large rate values approaches the Gaussian law, therefore its skewness

  17. Numbers and functional lateralization: A visual half-field and dichotic listening study in proficient bilinguals.

    Science.gov (United States)

    Klichowski, Michal; Króliczak, Gregory

    2017-06-01

    Potential links between language and numbers and the laterality of symbolic number representations in the brain are still debated. Furthermore, reports on bilingual individuals indicate that the language-number interrelationships might be quite complex. Therefore, we carried out a visual half-field (VHF) and dichotic listening (DL) study with action words and different forms of symbolic numbers used as stimuli to test the laterality of word and number processing in single-, dual-language and mixed -task and language- contexts. Experiment 1 (VHF) showed a significant right visual field/left hemispheric advantage in response accuracy for action word, as compared to any form of symbolic number processing. Experiment 2 (DL) revealed a substantially reversed effect - a significant right ear/left hemisphere advantage for arithmetic operations as compared to action word processing, and in response times in single- and dual-language contexts for number vs. action words. All these effects were language independent. Notably, for within-task response accuracy compared across modalities significant differences were found in all studied contexts. Thus, our results go counter to findings showing that action-relevant concepts and words, as well as number words are represented/processed primarily in the left hemisphere. Instead, we found that in the auditory context, following substantial engagement of working memory (here: by arithmetic operations), there is a subsequent functional reorganization of processing single stimuli, whether verbs or numbers. This reorganization - their weakened laterality - at least for response accuracy is not exclusive to processing of numbers, but the number of items to be processed. For response times, except for unpredictable tasks in mixed contexts, the "number problem" is more apparent. These outcomes are highly relevant to difficulties that simultaneous translators encounter when dealing with lengthy auditory material in which single items such

  18. Volume 9 Number 3

    African Journals Online (AJOL)

    OLUWOLE

    Volume 9 Number 3 September 2010 pp. 200 - 208. ISSN 1119-7455. EFFECTS OF PROCESSING METHODS ON THE CHEMICAL. COMPOSITION OF FLOUR, MOINMOIN AND AKARA FROM Mucuna pruriens. Asogwa, I.S 1and Onweluzo, J.C2. 1Dept. of Food Science and Technology, University of Mkar, Benue State, ...

  19. The Congruent Number Problem

    Indian Academy of Sciences (India)

    indebtedness to his remote predecessor. Since t/l.en the theory of elliptic curves, and its genemlizations to curves of higher genus and to abelian varieties, has bee?1 one of the main topics of modern number theory. Fermat's name, and his method of infinite desce1}-t, are indissolubly bound with it; they promise to remain so ...

  20. Factoring Fermat Numbers

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 1. Factoring Fermat Numbers. C E Veni Madhavan. Research News Volume 1 Issue 1 January 1996 pp 108-108. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/001/01/0108-0108. Author Affiliations.

  1. The Class Number Problem

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 3; Issue 6. The Class Number Problem - Binary Quadratic Forms. Rajat Tandon. General Article Volume 3 Issue ... Author Affiliations. Rajat Tandon1. Department of Mathematics, University of Hyderabad, Central University P.O. Hyderabad 500 046. India ...

  2. The Mystery of Numbers

    Indian Academy of Sciences (India)

    It was proved in the nineteenth century that the number of primes less than or equal to n approaches n/logn as n becomes very large. With modern computing and cryptography, the search for large primes has gained further impe- tus. Expected to find a prime with 10 million digits within a year... – p.22/22.

  3. Littlewood and Number Theory

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 18; Issue 9. Littlewood and Number Theory. M Ram Murty. General Article Volume 18 Issue 9 September 2013 pp 789-798. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/018/09/0789-0798. Keywords.

  4. Introducing Complex Numbers

    Science.gov (United States)

    Trudgian, Timothy

    2009-01-01

    One of the difficulties in any teaching of mathematics is to bridge the divide between the abstract and the intuitive. Throughout school one encounters increasingly abstract notions, which are more and more difficult to relate to everyday experiences. This article examines a familiar approach to thinking about negative numbers, that is an…

  5. The magic of numbers

    CERN Document Server

    Bell, Eric Temple

    1991-01-01

    From one of the foremost interpreters for lay readers of the history and meaning of mathematics: a stimulating account of the origins of mathematical thought and the development of numerical theory. It probes the work of Pythagoras, Galileo, Berkeley, Einstein, and others, exploring how ""number magic"" has influenced religion, philosophy, science, and mathematics

  6. Colour by Numbers

    Science.gov (United States)

    Wetherell, Chris

    2017-01-01

    This is an edited extract from the keynote address given by Dr. Chris Wetherell at the 26th Biennial Conference of the Australian Association of Mathematics Teachers Inc. The author investigates the surprisingly rich structure that exists within a simple arrangement of numbers: the times tables.

  7. Paint by Numbers Revived!

    Science.gov (United States)

    Hahn, Nic

    2012-01-01

    Remember paint by numbers? This revived trend was a perfect solution to teaching geometric shapes to the author's first-grade students. Geometric shapes are identified and used in early elementary art classrooms, but this lesson gives students a deeper understanding of shape, encourages problem-solving, and makes a strong correlation between math…

  8. Number Theory and Combinatorics

    Indian Academy of Sciences (India)

    2012-02-24

    Feb 24, 2012 ... able to a motivated undergraduate or postgraduate student. It may be somewhat of a challenge to make it ...... A quote attributed to the famous mathematician L Kronecker is 'Die. Ganzen Zahlen hat Gott gemacht, alles ...... Interestingly, Bertrand's motivation was to group theory and not really number theory ...

  9. Physical Constraints of Numbers

    OpenAIRE

    Mueckenheim, W.

    2005-01-01

    All sciences need and many arts apply mathematics whereas mathematics seems to be independent of all of them, but only based upon logic. This conservative concept, however, needs to be revised because, contrary to Platonic idealism (frequently called "realism" by mathematicians), mathematical ideas, notions, and, in particular, numbers are not at all independent of physical laws and prerequisites.

  10. Biting into Big Numbers.

    Science.gov (United States)

    Anderson, Maureen McCahan

    1996-01-01

    A mnemonic clue sentence--"He thinks mice bite trees"--is suggested for helping students with learning disabilities or mild mental retardation successfully identify up to 15 digit numbers by relating the sentence to the sequence of hundreds, thousands, millions, billions, and trillions. (DB)

  11. Fermion Number Fractionization

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 8. Fermion Number Fractionization. Kumar Rao Narendra Sahu Prasanta K ... Author Affiliations. Kumar Rao1 Narendra Sahu1 Prasanta K Panigrahi1. Theoretical Physics Division, Physical Research Laboratory, Ahmedabad 380 009, India ...

  12. Factoring Fermat Numbers

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 1. Factoring Fermat Numbers. C E Veni Madhavan. Research News Volume 1 Issue 1 January 1996 pp 108-108. Fulltext. Click here to view fulltext PDF. Permanent link: https://www.ias.ac.in/article/fulltext/reso/001/01/0108-0108 ...

  13. ALARA notes, Number 8

    International Nuclear Information System (INIS)

    Khan, T.A.; Baum, J.W.; Beckman, M.C.

    1993-10-01

    This document contains information dealing with the lessons learned from the experience of nuclear plants. In this issue the authors tried to avoid the 'tyranny' of numbers and concentrated on the main lessons learned. Topics include: filtration devices for air pollution abatement, crack repair and inspection, and remote handling equipment

  14. Volume 9 Number 3

    African Journals Online (AJOL)

    OLUWOLE

    separately to eggs in the hatch; every treatment was replicated eight times. Observations on cumulative egg hatch were made every 24 hours for six consecutive days. This was done by counting the number of second stage juvenile which emerged from egg using stereomicroscope. Juvenile mortality observation: Ten ...

  15. The Brothel Phone Number

    DEFF Research Database (Denmark)

    Korsby, Trine Mygind

    2017-01-01

    in turn cultivate and maximize uncertainty about themselves in others. When making the move to go abroad into unknown terrains, accessing the infrastructure generated by the phone number can provide certainty and consolidate one’s position within criminal networks abroad. However, at the same time...

  16. Uniform random number generators

    Science.gov (United States)

    Farr, W. R.

    1971-01-01

    Methods are presented for the generation of random numbers with uniform and normal distributions. Subprogram listings of Fortran generators for the Univac 1108, SDS 930, and CDC 3200 digital computers are also included. The generators are of the mixed multiplicative type, and the mathematical method employed is that of Marsaglia and Bray.

  17. Typical Complexity Numbers

    Indian Academy of Sciences (India)

    First page Back Continue Last page Overview Graphics. Typical Complexity Numbers. Say. 1000 tones,; 100 Users,; Transmission every 10 msec. Full Crosstalk cancellation would require. Full cancellation requires a matrix multiplication of order 100*100 for all the tones. 1000*100*100*100 operations every second for the ...

  18. Predicting Lotto Numbers

    NARCIS (Netherlands)

    Jorgensen, C.B.; Suetens, S.; Tyran, J.R.

    2011-01-01

    We investigate the "law of small numbers" using a unique panel data set on lotto gambling. Because we can track individual players over time, we can measure how they react to outcomes of recent lotto drawings. We can therefore test whether they behave as if they believe they can predict lotto

  19. Number Theory and Combinatorics

    Indian Academy of Sciences (India)

    cles on Number Theory and Combinatorics comprise the present book. He ..... Galois theory. In the case of the circle, the Galois group of the cyclotomic extension is the multiplicative group of integers modulo n which are coprime to n. This latter group is ...... Pillai proves that when t = n and the game is carefully played, then it.

  20. Numbers and sets

    Directory of Open Access Journals (Sweden)

    Marco Ruffino

    2001-12-01

    Full Text Available In this paper I discuss the intuition behind Frege's and Russell's definitions of numbers as sets, as well as Benacerraf's criticism of it. I argue that Benacerraf's argument is not as strong as some philosophers tend to think. Moreover, I examine an alternative to the Fregean-Russellian definition of numbers proposed by Maddy, and point out some problems faced by it.Neste artigo discuto a intuição subjacente à definição de n∨meros como conjuntos proposta por Frege e Russell, assim como a crítica de Benacerraf a esta definição. Eu tento mostrar que o argumento de Benacerraf não é tão forte como alguns filósofos o tomaram. Adicionalmente, examino uma alternativa à definição de Frege e Russell proposta por Maddy, e indico algumas dificuldades encontrada pela mesma.

  1. Chromosome numbers in Bromeliaceae

    OpenAIRE

    Cotias-de-Oliveira,Ana Lúcia Pires; Assis,José Geraldo Aquino de; Bellintani,Moema Cortizo; Andrade,Jorge Clarêncio Souza; Guedes,Maria Lenise Silva

    2000-01-01

    The present study reports chromosome numbers of 17 species of Bromeliaceae, belonging to the genera Encholirium, Bromelia, Orthophytum, Hohenbergia, Billbergia, Neoglaziovia, Aechmea, Cryptanthus and Ananas. Most species present 2n = 50, however, Bromelia laciniosa, Orthophytum burle-marxii and O. maracasense are polyploids with 2n = 150, 2n = 100 and 2n = 150, respectively, while for Cryptanthus bahianus, 2n = 34 + 1-4B. B chromosomes were observed in Bromelia plumieri and Hohenbergia aff. u...

  2. Number Needed To… $ave?

    Science.gov (United States)

    Rocker, Graeme M; Verma, Jennifer Y; Demmons, Jillian; Mittmann, Nicole

    2015-02-06

    The 'Number Needed to Treat' (NNT) is a useful measure for estimating the number of patients that would need to receive a therapeutic intervention to avoid one of the adverse events that the treatment is designed to prevent. We explored the possibility of an adaption of NNT to estimate the 'Number Needed to $ave' (NN$) as a new, conceptual systems metric to estimate potential cost-savings to the health system from implementation of a treatment, or in this case, a program. We used the outcomes of the INSPIRED COPD Outreach ProgramTM to calculate that 26 patients would need to complete the program to avoid healthcare expenditures of $100,000, based on hospital bed days avoided. The NN$ does not translate into 'cost savings' per se, but redirection of resource expenditures for other purposes. We propose that the NN$ metric, if further developed, could help to inform system-level resource allocation decisions in a manner similar to the way that the NNT metric helps to inform individual-level treatment decisions.

  3. The number system

    CERN Document Server

    Thurston, H A

    2007-01-01

    The teaching of mathematics has undergone extensive changes in approach, with a shift in emphasis from rote memorization to acquiring an understanding of the logical foundations and methodology of problem solving. This book offers guidance in that direction, exploring arithmetic's underlying concepts and their logical development.This volume's great merit lies in its wealth of explanatory material, designed to promote an informal and intuitive understanding of the rigorous logical approach to the number system. The first part explains and comments on axioms and definitions, making their subseq

  4. On Dimensionless Numbers

    Czech Academy of Sciences Publication Activity Database

    Růžička, Marek

    2008-01-01

    Roč. 86, č. 8A (2008), s. 835-868 ISSN 0263-8762 R&D Projects: GA ČR GA104/06/1418; GA ČR GA104/07/1110; GA AV ČR IAAX00130702; GA AV ČR(CZ) IAA200720801; GA MŠk ME 952 Institutional research plan: CEZ:AV0Z40720504 Keywords : dimensionless numbers * dimensional analysis * scaling of equation s Subject RIV: CI - Industrial Chemistry, Chemical Engineering Impact factor: 0.989, year: 2008

  5. Topics in number theory

    CERN Document Server

    LeVeque, William J

    2002-01-01

    Classic two-part work now available in a single volume assumes no prior theoretical knowledge on reader's part and develops the subject fully. Volume I is a suitable first course text for advanced undergraduate and beginning graduate students. Volume II requires a much higher level of mathematical maturity, including a working knowledge of the theory of analytic functions. Contents range from chapters on binary quadratic forms to the Thue-Siegel-Roth Theorem and the Prime Number Theorem. Includes numerous problems and hints for their solutions. 1956 edition. Supplementary Reading. List of Symb

  6. Fulltext PDF

    Indian Academy of Sciences (India)

    emphasise(s) reasonably stable fundamental ideas on which ... (information) technology is built and evolves. It does ... if one deals with hexadecimal numbers system in which there are 16 (24) basic numbers. To store images we need ... deal with software. Beginning with operating systems and basic input output systems.

  7. Number Theoretic Background

    Science.gov (United States)

    Rudnick, Z.

    Contents: 1. Introduction 2. Divisibility 2.1. Basics on Divisibility 2.2. The Greatest Common Divisor 2.3. The Euclidean Algorithm 2.4. The Diophantine Equation ax+by=c 3. Prime Numbers 3.1. The Fundamental Theorem of Arithmetic 3.2. There Are Infinitely Many Primes 3.3. The Density of Primes 3.4. Primes in Arithmetic Progressions 4. Continued Fractions 5. Modular Arithmetic 5.1. Congruences 5.2. Modular Inverses 5.3. The Chinese Remainder Theorem 5.4. The Structure of the Multiplicative Group (Z/NZ)^* 5.5. Primitive Roots 6. Quadratic Congruences 6.1. Euler's Criterion 6.2. The Legendre Symbol and Quadratic Reciprocity 7. Pell's Equation 7.1. The Group Law 7.2. Integer Solutions 7.3. Finding the Fundamental Solution 8. The Riemann Zeta Function 8.1 Analytic Continuation and Functinal Equation of ζ(s) 8.2 Connecting the Primes and the Zeros of ζ(s) 8.3 The Riemann Hypothesis References

  8. [The power of numbers].

    Science.gov (United States)

    van Gijn, J

    2000-01-01

    The round figure for the current year has stirred people's minds in anticipation. Numbers have acquired great significance also in today's medical science. The Paris physician Pierre Charles Alexandre Louis (1787-1872) is considered the founding father of the numerical method in medicine. At first the principle of aggregating data from different individuals aroused much resistance and even disgust: Claude Bernard was a leading figure among those who warned that one will never find a mean in nature, and that grouping findings together obscures the true relationship between biological phenomena. True enough, statistical significance is not a characteristic of nature itself. Significant differences or risk reductions do not necessarily imply clinical relevance, and results obtained in a group of patients are rarely applicable to an individual patient in the consultation room. Likewise, the health of a human being cannot be captured in biochemical, radiological or other technical measures, nor in disease-specific scales that reduce well-being to one or two digits. The editors of this journal will remain keen on publishing numerical studies that contribute to evidence-based medicine, but at the same time they will continue to foster the art of reporting illness from the point of view of the sick person.

  9. Author Details

    African Journals Online (AJOL)

    Obidunnu, NJ. Vol 15, No 2 (2009) - Articles The Inverted-Triangle Technique Of Converting The Computer Number Systems (Binary, Octal And Hexadecimal) To Decimal Abstract. ISSN: 1118-0579. AJOL African Journals Online. HOW TO USE AJOL... for Researchers · for Librarians · for Authors · FAQ's · More about AJOL ...

  10. Defense AT&L (Volume 35, Number 5, September-October 2006)

    National Research Council Canada - National Science Library

    2006-01-01

    .... "Transitioning an ACTD to an Acquisition Program," by Col. G. Scott Coale, et al. -- Rapid transition of Global Hawk from the ACTD phase into formal acquisition has broken the historical paradigm of lengthy acquisition cycle time...

  11. [Intel random number generator-based true random number generator].

    Science.gov (United States)

    Huang, Feng; Shen, Hong

    2004-09-01

    To establish a true random number generator on the basis of certain Intel chips. The random numbers were acquired by programming using Microsoft Visual C++ 6.0 via register reading from the random number generator (RNG) unit of an Intel 815 chipset-based computer with Intel Security Driver (ISD). We tested the generator with 500 random numbers in NIST FIPS 140-1 and X(2) R-Squared test, and the result showed that the random number it generated satisfied the demand of independence and uniform distribution. We also compared the random numbers generated by Intel RNG-based true random number generator and those from the random number table statistically, by using the same amount of 7500 random numbers in the same value domain, which showed that the SD, SE and CV of Intel RNG-based random number generator were less than those of the random number table. The result of u test of two CVs revealed no significant difference between the two methods. Intel RNG-based random number generator can produce high-quality random numbers with good independence and uniform distribution, and solves some problems with random number table in acquisition of the random numbers.

  12. Cordial Languages and Cordial Numbers

    Directory of Open Access Journals (Sweden)

    J. Baskar BABUJEE

    2012-01-01

    Full Text Available The concept of cordial labeling in graphs motivated us to introduce cordial words, cordial languages and cordial numbers. We interpret the notion of cordial labeling in Automata and thereby study the corresponding languages. In this paper we develop a new sequence of numbers called the cordial numbers in number theory using the labeling techniques in graph theory on automata theory.

  13. Bell numbers, determinants and series

    Indian Academy of Sciences (India)

    In this article, we study Bell numbers and Uppuluri Carpenter numbers. We obtain various expressions and relations between them. These include polynomial recurrences and expressions as determinants of certain matrices of binomial coefficients. Keywords. p-adic series; Bell numbers. 1. Introduction. Bell numbers, Bn [2] ...

  14. Cosmic numbers the numbers that define our universe

    CERN Document Server

    Stein, James D

    2011-01-01

    Our fascination with numbers begins when we are children and continues throughout our lives. We start counting our fingers and toes and end up balancing checkbooks and calculating risk. So powerful is the appeal of numbers that many people ascribe to them a mystical significance. Other numbers go beyond the supernatural, working to explain our universe and how it behaves. In Cosmic Numbers , mathematics professor James D. Stein traces the discovery, evolution, and interrelationships of the numbers that define our world. Everyone knows about the speed of light and absolute zero, but numbers lik

  15. Fermion number in supersymmetric models

    International Nuclear Information System (INIS)

    Mainland, G.B.; Tanaka, K.

    1975-01-01

    The two known methods for introducing a conserved fermion number into supersymmetric models are discussed. While the introduction of a conserved fermion number often requires that the Lagrangian be massless or that bosons carry fermion number, a model is discussed in which masses can be introduced via spontaneous symmetry breaking and fermion number is conserved at all stages without assigning fermion number to bosons. (U.S.)

  16. THE RELATIONSHIP BETWEEN NUMBER NAMES AND NUMBER CONCEPTS

    DEFF Research Database (Denmark)

    Ejersbo, Lisser Rye; Misfeldt, Morten

    Different countries have different names for numbers. These names are often related in a regular way to the base-10 place value system used for writing numbers as digits. However, in several languages, this regularity breaks down (e.g., between 10 and 20), and there is limited knowledge of how...... the regularity or irregularity of number naming affects children’s formation of number concepts and arithmetic performance. We investigate this issue by reviewing relevant literature and undertaking a design research project addressing the specific irregularities of the Danish number names. In this project......, a second, regular set of number names is introduced in primary school. The study’s findings suggest that the regularity of number names influences the development of number concepts and creates a positive impact on the understanding of the base-10 system....

  17. How Spencer Made Number: First Uses of the Number Words

    Science.gov (United States)

    Mix, Kelly S.

    2009-01-01

    This article describes the development of number concepts between infancy and early childhood. It is based on a diary study that tracked number word use in a child from 12 to 38 months of age. Number words appeared early in the child's vocabulary, but accurate reference to specific numerosities evolved gradually over the entire 27-month period.…

  18. Number games, magnitude representation, and basic number skills in preschoolers.

    Science.gov (United States)

    Whyte, Jemma Catherine; Bull, Rebecca

    2008-03-01

    The effect of 3 intervention board games (linear number, linear color, and nonlinear number) on young children's (mean age = 3.8 years) counting abilities, number naming, magnitude comprehension, accuracy in number-to-position estimation tasks, and best-fit numerical magnitude representations was examined. Pre- and posttest performance was compared following four 25-min intervention sessions. The linear number board game significantly improved children's performance in all posttest measures and facilitated a shift from a logarithmic to a linear representation of numerical magnitude, emphasizing the importance of spatial cues in estimation. Exposure to the number card games involving nonsymbolic magnitude judgments and association of symbolic and nonsymbolic quantities, but without any linear spatial cues, improved some aspects of children's basic number skills but not numerical estimation precision.

  19. Why do general medical patients have a lengthy wait in the emergency department before admission?

    Directory of Open Access Journals (Sweden)

    Nin-Chieh Hsu

    2014-08-01

    Conclusion: Complex comorbidities and terminal conditions with DNR consent were associated with the prolonged ED stay for general medical patients. The hospital manager should pay attention to general medical patients with multiple comorbidities as well as those who require palliative care.

  20. When lives are put on hold: Lengthy asylum processes decrease employment among refugees

    Science.gov (United States)

    Hainmueller, Jens; Hangartner, Dominik; Lawrence, Duncan

    2016-01-01

    European governments are struggling with the biggest refugee crisis since World War II, but there exists little evidence regarding how the management of the asylum process affects the subsequent integration of refugees in the host country. We provide new causal evidence about how one central policy parameter, the length of time that refugees wait in limbo for a decision on their asylum claim, affects their subsequent economic integration. Exploiting exogenous variation in wait times and registry panel data covering refugees who applied in Switzerland between 1994 and 2004, we find that one additional year of waiting reduces the subsequent employment rate by 4 to 5 percentage points, a 16 to 23% drop compared to the average rate. This deleterious effect is remarkably stable across different subgroups of refugees stratified by gender, origin, age at arrival, and assigned language region, a pattern consistent with the idea that waiting in limbo dampens refugee employment through psychological discouragement, rather than a skill atrophy mechanism. Overall, our results suggest that marginally reducing the asylum waiting period can help reduce public expenditures and unlock the economic potential of refugees by increasing employment among this vulnerable population. PMID:27493995

  1. Closing the Door Behind You: How the United States Army Conducts Logistical Withdrawals after Lengthy Operations

    Science.gov (United States)

    2013-05-23

    AirLand Battle doctrine. It remains an active Field Manual. FM 100-9 details the steps to regenerate combat power after extensive attrition by enemy...peace talks in Paris . After a heavy bombing campaign against North Vietnam forced a resumption of negotiations, the United States agreed to a cease-fire...march to Baghdad, hindered mobility throughout urban areas and stability operations. CJTF-7 leaders saw that additional forces would be required to

  2. When lives are put on hold: Lengthy asylum processes decrease employment among refugees.

    Science.gov (United States)

    Hainmueller, Jens; Hangartner, Dominik; Lawrence, Duncan

    2016-08-01

    European governments are struggling with the biggest refugee crisis since World War II, but there exists little evidence regarding how the management of the asylum process affects the subsequent integration of refugees in the host country. We provide new causal evidence about how one central policy parameter, the length of time that refugees wait in limbo for a decision on their asylum claim, affects their subsequent economic integration. Exploiting exogenous variation in wait times and registry panel data covering refugees who applied in Switzerland between 1994 and 2004, we find that one additional year of waiting reduces the subsequent employment rate by 4 to 5 percentage points, a 16 to 23% drop compared to the average rate. This deleterious effect is remarkably stable across different subgroups of refugees stratified by gender, origin, age at arrival, and assigned language region, a pattern consistent with the idea that waiting in limbo dampens refugee employment through psychological discouragement, rather than a skill atrophy mechanism. Overall, our results suggest that marginally reducing the asylum waiting period can help reduce public expenditures and unlock the economic potential of refugees by increasing employment among this vulnerable population.

  3. Elliptic Curves and Number Theory

    Indian Academy of Sciences (India)

    R. Sujatha, School of Mathematics, Tata Institute of Fundamental Research, Mumbai, INDIA

    1. Aim: To explain the connection between a simple ancient problem in number theory and a deep sophisticated conjecture about Elliptic Curves. ('arithmetic Geometry'). Notation: N : set of natural numbers (1,2,3,...) ...

  4. Bell numbers, determinants and series

    Indian Academy of Sciences (India)

    In this article, we study Bell numbers and Uppuluri Carpenter numbers. We obtain various expressions and relations between them. These include polynomial recurrences and expressions as determinants of certain matrices of binomial coefficients.

  5. Elementary number theory with programming

    CERN Document Server

    Lewinter, Marty

    2015-01-01

    A successful presentation of the fundamental concepts of number theory and computer programming Bridging an existing gap between mathematics and programming, Elementary Number Theory with Programming provides a unique introduction to elementary number theory with fundamental coverage of computer programming. Written by highly-qualified experts in the fields of computer science and mathematics, the book features accessible coverage for readers with various levels of experience and explores number theory in the context of programming without relying on advanced prerequisite knowledge and con

  6. Distribution theory of algebraic numbers

    CERN Document Server

    Yang, Chung-Chun

    2008-01-01

    The book timely surveys new research results and related developments in Diophantine approximation, a division of number theory which deals with the approximation of real numbers by rational numbers. The book is appended with a list of challenging open problems and a comprehensive list of references. From the contents: Field extensions Algebraic numbers Algebraic geometry Height functions The abc-conjecture Roth''s theorem Subspace theorems Vojta''s conjectures L-functions.

  7. Random Numbers and Quantum Computers

    Science.gov (United States)

    McCartney, Mark; Glass, David

    2002-01-01

    The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since…

  8. 2016 Gainesville Number Theory Conference

    CERN Document Server

    Garvan, Frank

    2017-01-01

    Gathered from the 2016 Gainesville Number Theory Conference honoring Krishna Alladi on his 60th birthday, these proceedings present recent research in number theory. Extensive and detailed, this volume features 40 articles by leading researchers on topics in analytic number theory, probabilistic number theory, irrationality and transcendence, Diophantine analysis, partitions, basic hypergeometric series, and modular forms. Readers will also find detailed discussions of several aspects of the path-breaking work of Srinivasa Ramanujan and its influence on current research. Many of the papers were motivated by Alladi's own research on partitions and q-series as well as his earlier work in number theory.  Alladi is well known for his contributions in number theory and mathematics. His research interests include combinatorics, discrete mathematics, sieve methods, probabilistic and analytic number theory, Diophantine approximations, partitions and q-series identities. Graduate students and researchers will find th...

  9. Children's mappings between number words and the approximate number system.

    Science.gov (United States)

    Odic, Darko; Le Corre, Mathieu; Halberda, Justin

    2015-05-01

    Humans can represent number either exactly--using their knowledge of exact numbers as supported by language, or approximately--using their approximate number system (ANS). Adults can map between these two systems--they can both translate from an approximate sense of the number of items in a brief visual display to a discrete number word estimate (i.e., ANS-to-Word), and can generate an approximation, for example by rapidly tapping, when provided with an exact verbal number (i.e., Word-to-ANS). Here we ask how these mappings are initially formed and whether one mapping direction may become functional before the other during development. In two experiments, we gave 2-5 year old children both an ANS-to-Word task, where they had to give a verbal number response to an approximate presentation (i.e., after seeing rapidly flashed dots, or watching rapid hand taps), and a Word-to-ANS task, where they had to generate an approximate response to a verbal number request (i.e., rapidly tapping after hearing a number word). Replicating previous results, children did not successfully generate numerically appropriate verbal responses in the ANS-to-Word task until after 4 years of age--well after they had acquired the Cardinality Principle of verbal counting. In contrast, children successfully generated numerically appropriate tapping sequences in the Word-to-ANS task before 4 years of age--well before many understood the Cardinality Principle. We further found that the accuracy of the mapping between the ANS and number words, as captured by error rates, continues to develop after this initial formation of the interface. These results suggest that the mapping between the ANS and verbal number representations is not functionally bidirectional in early development, and that the mapping direction from number representations to the ANS is established before the reverse. Copyright © 2015 Elsevier B.V. All rights reserved.

  10. On Fibonacci Numbers Which Are Elliptic Korselt Numbers

    Science.gov (United States)

    2014-11-17

    On Fibonacci numbers which are elliptic Korselt numbers Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South...is a CM elliptic curve with CM field Q( √ −d), then the set of n for which the nth Fibonacci number Fn satisfies an elliptic Korselt criterion for Q...Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that

  11. Photon number projection using non-number-resolving detectors

    International Nuclear Information System (INIS)

    Rohde, Peter P; Webb, James G; Huntington, Elanor H; Ralph, Timothy C

    2007-01-01

    Number-resolving photo-detection is necessary for many quantum optics experiments, especially in the application of entangled state preparation. Several schemes have been proposed for approximating number-resolving photo-detection using non-number-resolving detectors. Such techniques include multi-port detection and time-division multiplexing. We provide a detailed analysis and comparison of different number-resolving detection schemes, with a view to creating a useful reference for experimentalists. We show that the ideal architecture for projective measurements is a function of the detector's dark count and efficiency parameters. We also describe a process for selecting an appropriate topology given actual experimental component parameters

  12. Bernoulli numbers and zeta functions

    CERN Document Server

    Arakawa, Tsuneo; Kaneko, Masanobu

    2014-01-01

    Two major subjects are treated in this book. The main one is the theory of Bernoulli numbers and the other is the theory of zeta functions. Historically, Bernoulli numbers were introduced to give formulas for the sums of powers of consecutive integers. The real reason that they are indispensable for number theory, however, lies in the fact that special values of the Riemann zeta function can be written by using Bernoulli numbers. This leads to more advanced topics, a number of which are treated in this book: Historical remarks on Bernoulli numbers and the formula for the sum of powers of consecutive integers; a formula for Bernoulli numbers by Stirling numbers; the Clausen–von Staudt theorem on the denominators of Bernoulli numbers; Kummer's congruence between Bernoulli numbers and a related theory of p-adic measures; the Euler–Maclaurin summation formula; the functional equation of the Riemann zeta function and the Dirichlet L functions, and their special values at suitable integers; various formulas of ...

  13. Compendium of Experimental Cetane Numbers

    Energy Technology Data Exchange (ETDEWEB)

    Yanowitz, Janet [Ecoengineering, Sharonville, OH (United States); Ratcliff, Matthew A. [National Renewable Energy Lab. (NREL), Golden, CO (United States); McCormick, Robert L. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Taylor, J. D. [National Renewable Energy Lab. (NREL), Golden, CO (United States); Murphy, M. J. [Battelle, Columbus, OH (United States)

    2017-02-22

    This report is an updated version of the 2014 Compendium of Experimental Cetane Number Data and presents a compilation of measured cetane numbers for pure chemical compounds. It includes all available single-compound cetane number data found in the scientific literature up until December 2016 as well as a number of previously unpublished values, most measured over the past decade at the National Renewable Energy Laboratory. This version of the compendium contains cetane values for 496 pure compounds, including 204 hydrocarbons and 292 oxygenates. 176 individual measurements are new to this version of the compendium, all of them collected using ASTM Method D6890, which utilizes an Ignition Quality Tester (IQT) a type of constant-volume combustion chamber. For many compounds, numerous measurements are included, often collected by different researchers using different methods. The text of this document is unchanged from the 2014 version, except for the numbers of compounds in Section 3.1, the Appendices, Table 1. Primary Cetane Number Data Sources and Table 2. Number of Measurements Included in Compendium. Cetane number is a relative ranking of a fuel's autoignition characteristics for use in compression ignition engines. It is based on the amount of time between fuel injection and ignition, also known as ignition delay. The cetane number is typically measured either in a single-cylinder engine or a constant-volume combustion chamber. Values in the previous compendium derived from octane numbers have been removed and replaced with a brief analysis of the correlation between cetane numbers and octane numbers. The discussion on the accuracy and precision of the most commonly used methods for measuring cetane number has been expanded, and the data have been annotated extensively to provide additional information that will help the reader judge the relative reliability of individual results.

  14. THE RELATIONSHIP BETWEEN NUMBER NAMES AND NUMBER CONCEPTS

    DEFF Research Database (Denmark)

    Ejersbo, Lisser Rye; Misfeldt, Morten

    2016-01-01

    Different countries have different names for numbers. These names are often related in a regular way to the base-10 place value system used for writing numbers as digits. However, in several languages, this regularity breaks down (e.g., between 10 and 20), and there is limited knowledge of how...

  15. Reprint Series: Prime Numbers and Perfect Numbers. RS-2.

    Science.gov (United States)

    Schaaf, William L., Ed.

    This is one in a series of SMSG supplementary and enrichment pamphlets for high school students. This series makes available expository articles which appeared in a variety of mathematical periodicals. Topics covered include: (1) the prime numbers; (2) mathematical sieves; (3) the factorgram; and (4) perfect numbers. (MP)

  16. Dynamic Virtual Credit Card Numbers

    Science.gov (United States)

    Molloy, Ian; Li, Jiangtao; Li, Ninghui

    Theft of stored credit card information is an increasing threat to e-commerce. We propose a dynamic virtual credit card number scheme that reduces the damage caused by stolen credit card numbers. A user can use an existing credit card account to generate multiple virtual credit card numbers that are either usable for a single transaction or are tied with a particular merchant. We call the scheme dynamic because the virtual credit card numbers can be generated without online contact with the credit card issuers. These numbers can be processed without changing any of the infrastructure currently in place; the only changes will be at the end points, namely, the card users and the card issuers. We analyze the security requirements for dynamic virtual credit card numbers, discuss the design space, propose a scheme using HMAC, and prove its security under the assumption the underlying function is a PRF.

  17. Nonliteral understanding of number words.

    Science.gov (United States)

    Kao, Justine T; Wu, Jean Y; Bergen, Leon; Goodman, Noah D

    2014-08-19

    One of the most puzzling and important facts about communication is that people do not always mean what they say; speakers often use imprecise, exaggerated, or otherwise literally false descriptions to communicate experiences and attitudes. Here, we focus on the nonliteral interpretation of number words, in particular hyperbole (interpreting unlikely numbers as exaggerated and conveying affect) and pragmatic halo (interpreting round numbers imprecisely). We provide a computational model of number interpretation as social inference regarding the communicative goal, meaning, and affective subtext of an utterance. We show that our model predicts humans' interpretation of number words with high accuracy. Our model is the first to our knowledge to incorporate principles of communication and empirically measured background knowledge to quantitatively predict hyperbolic and pragmatic halo effects in number interpretation. This modeling framework provides a unified approach to nonliteral language understanding more generally.

  18. Number-unconstrained quantum sensing

    Science.gov (United States)

    Mitchell, Morgan W.

    2017-12-01

    Quantum sensing is commonly described as a constrained optimization problem: maximize the information gained about an unknown quantity using a limited number of particles. Important sensors including gravitational wave interferometers and some atomic sensors do not appear to fit this description, because there is no external constraint on particle number. Here, we develop the theory of particle-number-unconstrained quantum sensing, and describe how optimal particle numbers emerge from the competition of particle-environment and particle-particle interactions. We apply the theory to optical probing of an atomic medium modeled as a resonant, saturable absorber, and observe the emergence of well-defined finite optima without external constraints. The results contradict some expectations from number-constrained quantum sensing and show that probing with squeezed beams can give a large sensitivity advantage over classical strategies when each is optimized for particle number.

  19. Bell numbers, determinants and series

    Indian Academy of Sciences (India)

    k=0. (−1)k S(n, k). The usual generating functions for Bell numbers and complementary Bell numbers are given by. ∞. ∑ n=0. Bn tn n! = eet −1 and. ∞. ∑ n=0. ˜Bn tn n! = e−et +1. Stirling numbers can .... + 1) + gn−1(m − 1) = mn−1 + Bn(−1)n. Since there are infinitely many such m the required polynomial recurrence follows.

  20. Familial sinistrals avoid exact numbers.

    Directory of Open Access Journals (Sweden)

    Uli Sauerland

    Full Text Available We report data from an internet questionnaire of sixty number trivia. Participants were asked for the number of cups in their house, the number of cities they know and 58 other quantities. We compare the answers of familial sinistrals--individuals who are left-handed themselves or have a left-handed close blood-relative--with those of pure familial dextrals--right-handed individuals who reported only having right-handed close blood-relatives. We show that familial sinistrals use rounder numbers than pure familial dextrals in the survey responses. Round numbers in the decimal system are those that are multiples of powers of 10 or of half or a quarter of a power of 10. Roundness is a gradient concept, e.g. 100 is rounder than 50 or 200. We show that very round number like 100 and 1000 are used with 25% greater likelihood by familial sinistrals than by pure familial dextrals, while pure familial dextrals are more likely to use less round numbers such as 25, 60, and 200. We then use Sigurd's (1988, Language in Society index of the roundness of a number and report that familial sinistrals' responses are significantly rounder on average than those of pure familial dextrals. To explain the difference, we propose that the cognitive effort of using exact numbers is greater for the familial sinistral group because their language and number systems tend to be more distributed over both hemispheres of the brain. Our data support the view that exact and approximate quantities are processed by two separate cognitive systems. Specifically, our behavioral data corroborates the view that the evolutionarily older, approximate number system is present in both hemispheres of the brain, while the exact number system tends to be localized in only one hemisphere.

  1. Delannoy numbers and Legendre polytopes

    OpenAIRE

    Hetyei, Gábor

    2008-01-01

    International audience; We construct an $n$-dimensional polytope whose boundary complex is compressed and whose face numbers for any pulling triangulation are the coefficients of the powers of $(x-1)/2$ in the $n$-th Legendre polynomial. We show that the non-central Delannoy numbers count all faces in the lexicographic pulling triangulation that contain a point in a given open quadrant. We thus provide a geometric interpretation of a relation between the central Delannoy numbers and Legendre ...

  2. Some Generalized Harmonic Number Identities

    OpenAIRE

    Kronenburg, Maarten

    2011-01-01

    Summation by parts is used to find the sum of a finite series of generalized harmonic numbers involving a specific polynomial or rational function. The Euler-Maclaurin formula for sums of powers is used to find the sums of some finite series of generalized harmonic numbers involving nonnegative integer powers, which can be used to evaluate the sums of the finite series of generalized harmonic numbers involving polynomials. Many examples and a computer program are provided.

  3. Learning Potentials in Number Blocks

    DEFF Research Database (Denmark)

    Majgaard, Gunver; Misfeldt, Morten; Nielsen, Jacob

    2012-01-01

    . The tool is called Number Blocks and it combines physical interaction, learning, and immediate feedback. Number Blocks supports the children's understanding of place value in the sense that it allows them to experiment with creating large numbers. We found the blocks contributed to the learning process...... in several ways. The blocks combined mathematics and play, and they included and supported children at different academic levels. The auditory representation, especially the enhanced rhythmic effects due to using speech synthesis, and the rhythm helped the children to pronounce large numbers. This creates...

  4. A Research on a Certain Family of Numbers and Polynomials Related to Stirling Numbers, Central Factorial Numbers, and Euler Numbers

    Directory of Open Access Journals (Sweden)

    J. Y. Kang

    2013-01-01

    Full Text Available Recently, many mathematicians have studied different kinds of the Euler, Bernoulli, and Genocchi numbers and polynomials. In this paper, we give another definition of polynomials Ũn(x. We observe an interesting phenomenon of “scattering” of the zeros of the polynomials Ũn(x in complex plane. We find out some identities and properties related to polynomials Ũn(x. Finally, we also derive interesting relations between polynomials Ũn(x, Stirling numbers, central factorial numbers, and Euler numbers.

  5. Random number generation and creativity.

    Science.gov (United States)

    Bains, William

    2008-01-01

    A previous paper suggested that humans can generate genuinely random numbers. I tested this hypothesis by repeating the experiment with a larger number of highly numerate subjects, asking them to call out a sequence of digits selected from 0 through 9. The resulting sequences were substantially non-random, with an excess of sequential pairs of numbers and a deficit of repeats of the same number, in line with previous literature. However, the previous literature suggests that humans generate random numbers with substantial conscious effort, and distractions which reduce that effort reduce the randomness of the numbers. I reduced my subjects' concentration by asking them to call out in another language, and with alcohol - neither affected the randomness of their responses. This suggests that the ability to generate random numbers is a 'basic' function of the human mind, even if those numbers are not mathematically 'random'. I hypothesise that there is a 'creativity' mechanism, while not truly random, provides novelty as part of the mind's defence against closed programming loops, and that testing for the effects seen here in people more or less familiar with numbers or with spontaneous creativity could identify more features of this process. It is possible that training to perform better at simple random generation tasks could help to increase creativity, through training people to reduce the conscious mind's suppression of the 'spontaneous', creative response to new questions.

  6. The Algebra of Complex Numbers.

    Science.gov (United States)

    LePage, Wilbur R.

    This programed text is an introduction to the algebra of complex numbers for engineering students, particularly because of its relevance to important problems of applications in electrical engineering. It is designed for a person who is well experienced with the algebra of real numbers and calculus, but who has no experience with complex number…

  7. Counting copy number and calories.

    Science.gov (United States)

    White, Stefan

    2015-08-01

    Copy number variation (CNV) at several genomic loci has been associated with different human traits and diseases, but in many cases the findings could not be replicated. A new study provides insights into the degree of variation present at the amylase locus and calls into question a previous association between amylase copy number and body mass index.

  8. Generalized r-Lah numbers

    Indian Academy of Sciences (India)

    generalize earlier identities given for the r-Lah and r-Stirling numbers. We also pro- vide combinatorial proofs of some earlier identities involving the r-Lah numbers by defining appropriate sign-changing involutions. Generalizing these arguments yields orthogonality-type relations that are satisfied by Ga,b(n, k; r). Keywords.

  9. Number theory and its history

    CERN Document Server

    Ore, Oystein

    1988-01-01

    A prominent mathematician presents the principal ideas and methods of number theory within a historical and cultural framework. Oystein Ore's fascinating, accessible treatment requires only a basic knowledge of algebra. Topics include prime numbers, the Aliquot parts, linear indeterminate problems, congruences, Euler's theorem, classical construction problems, and many other subjects.

  10. On the Three Primordial Numbers

    NARCIS (Netherlands)

    Gobbetti, Roberto; Pajer, Enrico; Roest, Diederik

    2015-01-01

    Cosmological observations have provided us with the measurement of just three numbers that characterize the very early universe: $ 1-n_{s} $, $ N $ and $\\ln\\Delta_R^2$. Although each of the three numbers individually carries limited information about the physics of inflation, one may hope to extract

  11. Pseudo-Random Number Generators

    Science.gov (United States)

    Howell, L. W.; Rheinfurth, M. H.

    1984-01-01

    Package features comprehensive selection of probabilistic distributions. Monte Carlo simulations resorted to whenever systems studied not amenable to deterministic analyses or when direct experimentation not feasible. Random numbers having certain specified distribution characteristic integral part of simulations. Package consists of collector of "pseudorandom" number generators for use in Monte Carlo simulations.

  12. Core Knowledge, Language, and Number

    Science.gov (United States)

    Spelke, Elizabeth S.

    2017-01-01

    The natural numbers may be our simplest, most useful, and best-studied abstract concepts, but their origins are debated. I consider this debate in the context of the proposal, by Gallistel and Gelman, that natural number system is a product of cognitive evolution and the proposal, by Carey, that it is a product of human cultural history. I offer a…

  13. Investigating the Randomness of Numbers

    Science.gov (United States)

    Pendleton, Kenn L.

    2009-01-01

    The use of random numbers is pervasive in today's world. Random numbers have practical applications in such far-flung arenas as computer simulations, cryptography, gambling, the legal system, statistical sampling, and even the war on terrorism. Evaluating the randomness of extremely large samples is a complex, intricate process. However, the…

  14. Path-fan Ramsey numbers

    NARCIS (Netherlands)

    Salman, M.; Broersma, Haitze J.

    2003-01-01

    For two given graphs $G$ and $H$, the Ramsey number $R(G,H)$ is the smallest positive integer $p$ such that for every graph $F$ on $p$ vertices the following holds: either $F$ contains $G$ as a subgraph or the complement of $F$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers

  15. Path-fan Ramsey numbers

    NARCIS (Netherlands)

    Salman, M.; Broersma, Haitze J.

    For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers

  16. Path-kipas Ramsey numbers

    NARCIS (Netherlands)

    Salman, M.; Broersma, Haitze J.

    2007-01-01

    For two given graphs $F$ and $H$, the Ramsey number $R(F,H)$ is the smallest positive integer $p$ such that for every graph $G$ on $p$ vertices the following holds: either $G$ contains $F$ as a subgraph or the complement of $G$ contains $H$ as a subgraph. In this paper, we study the Ramsey numbers

  17. From natural numbers to quaternions

    CERN Document Server

    Kramer, Jürg

    2017-01-01

    This textbook offers an invitation to modern algebra through number systems of increasing complexity, beginning with the natural numbers and culminating with Hamilton's quaternions. Along the way, the authors carefully develop the necessary concepts and methods from abstract algebra: monoids, groups, rings, fields, and skew fields. Each chapter ends with an appendix discussing related topics from algebra and number theory, including recent developments reflecting the relevance of the material to current research. The present volume is intended for undergraduate courses in abstract algebra or elementary number theory. The inclusion of exercises with solutions also makes it suitable for self-study and accessible to anyone with an interest in modern algebra and number theory.

  18. Low energy fermion number violation

    International Nuclear Information System (INIS)

    Peccei, R.D.

    1989-01-01

    After a brief aside on charge quantization in the standard electroweak theory, I concentrate on various aspects of anomaly induced fermion number violation in the standard model. A critical analysis of the role of sphalerons for the universe's baryon asymmetry is presented and the importance of calculating directly fermion number violating Green's functions is stressed. A physical interpretation of the recent observation of Ringwald, that coherent effects in the electroweak theory lead to catastrophic fermion number violation at 100 TeV, is discussed. Possible quantum effects which might spoil this semi-classical picture are examined

  19. Gauged baryon and lepton numbers

    International Nuclear Information System (INIS)

    Foot, R.; Joshi, G.C.; Lew, H.

    1989-01-01

    A possible extension of the Standard Model can be defined by gauging the global baryon and lepton number U(1) symmetries. Gauging baryon and lepton numbers provide a natural framework for the see-saw mechanism in the lepton sector, and the Peccei-Quinn mechanism in the quark sector. Another consequence of this extension is that the usual three generations of fermions are not anomaly free. However the authors consider a wider framework involving the existence of generations with exotic SU(2) L tensor product U(1) Y quantum numbers. This allows them to derive a minimal spectrum of fermions which contain the known quarks and leptons. 12 refs

  20. Fundamental number theory with applications

    CERN Document Server

    Mollin, Richard A

    2008-01-01

    An update of the most accessible introductory number theory text available, Fundamental Number Theory with Applications, Second Edition presents a mathematically rigorous yet easy-to-follow treatment of the fundamentals and applications of the subject. The substantial amount of reorganizing makes this edition clearer and more elementary in its coverage. New to the Second Edition           Removal of all advanced material to be even more accessible in scope           New fundamental material, including partition theory, generating functions, and combinatorial number theory           Expa

  1. Number theory via Representation theory

    Indian Academy of Sciences (India)

    2014-11-09

    Number theory via Representation theory. Eknath Ghate. November 9, 2014. Eightieth Annual Meeting, Chennai. Indian Academy of Sciences1. 1. This is a non-technical 20 minute talk intended for a general Academy audience.

  2. Baryogenesis through lepton number violation

    CERN Document Server

    Sarkar, U

    1998-01-01

    The most promising scenarios of baryogenesis seems to be the one through lepton number violation. Lepton number violation through a Majarana mass of the right-handed neutrinos can generate a lepton asymmetry of the universe when the right-handed neutrinos decay. The left-handed neutrinos get small Majorana masses through see-saw mechanism in these models. A triplet higgs scalar violating lepton number explicitly through its couplings to two leptons or two higgs doublets can also naturally give small Majorana masses to the left-handed neutrinos and also generate a lepton asymmetry of the universe. We review both these models of leptogenesis, where the lepton number asymmetry then gets converted to a baryon asymmetry of the universe before the electroweak phase transition.

  3. Women In Numbers - Europe workshop

    CERN Document Server

    Bucur, Alina; Feigon, Brooke; Schneps, Leila

    2015-01-01

    Covering topics in graph theory, L-functions, p-adic geometry, Galois representations, elliptic fibrations, genus 3 curves and bad reduction, harmonic analysis, symplectic groups and mould combinatorics, this volume presents a collection of papers covering a wide swath of number theory emerging from the third iteration of the international Women in Numbers conference, “Women in Numbers - Europe” (WINE), held on October 14–18, 2013 at the CIRM-Luminy mathematical conference center in France. While containing contributions covering a wide range of cutting-edge topics in number theory, the volume emphasizes those concrete approaches that make it possible for graduate students and postdocs to begin work immediately on research problems even in highly complex subjects.

  4. SEVIS By the Numbers 2014

    Data.gov (United States)

    Department of Homeland Security — SEVIS by the Numbers is a quarterly report that highlights nonimmigrant student and exchange visitor trends, values and information using data from the Student and...

  5. Advanced number theory with applications

    CERN Document Server

    Mollin, Richard A

    2009-01-01

    Algebraic Number Theory and Quadratic Fields Algebraic Number Fields The Gaussian Field Euclidean Quadratic Fields Applications of Unique Factorization Ideals The Arithmetic of Ideals in Quadratic Fields Dedekind Domains Application to Factoring Binary Quadratic Forms Basics Composition and the Form Class Group Applications via Ambiguity Genus Representation Equivalence Modulo p Diophantine Approximation Algebraic and Transcendental Numbers Transcendence Minkowski's Convex Body Theorem Arithmetic Functions The Euler-Maclaurin Summation Formula Average Orders The Riemann zeta-functionIntroduction to p-Adic AnalysisSolving Modulo pn Introduction to Valuations Non-Archimedean vs. Archimedean Valuations Representation of p-Adic NumbersDirichlet: Characters, Density, and Primes in Progression Dirichlet Characters Dirichlet's L-Function and Theorem Dirichlet DensityApplications to Diophantine Equations Lucas-Lehmer Theory Generalized Ramanujan-Nagell Equations Bachet's Equation The Fermat Equation Catalan and the A...

  6. From Calculus to Number Theory

    Indian Academy of Sciences (India)

    A. Raghuram

    2016-11-04

    Nov 4, 2016 ... General L-functions. There are various mathematical objects M that determine, and are determined, by a sequence an = an(M). A general principle in number theory: study M by studying: ...

  7. Numbers their history and meaning

    CERN Document Server

    Flegg, Graham

    2003-01-01

    Readable, jargon-free book examines the earliest endeavors to count and record numbers, initial attempts to solve problems by using equations, and origins of infinite cardinal arithmetic. "Surprisingly exciting." - Choice.

  8. Poison control center - emergency number

    Science.gov (United States)

    For a POISON EMERGENCY call: 1-800-222-1222 ANYWHERE IN THE UNITED STATES This national hotline number will let you ... is a free and confidential service. All local poison control centers in the United States use this ...

  9. SEVIS By the Numbers 2016

    Data.gov (United States)

    Department of Homeland Security — SEVIS by the Numbers is a quarterly report that highlights nonimmigrant student and exchange visitor trends, values and information using data from the Student and...

  10. Classical theory of algebraic numbers

    CERN Document Server

    Ribenboim, Paulo

    2001-01-01

    Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...

  11. Microcomputer Unit: Generating Random Numbers.

    Science.gov (United States)

    Haigh, William E.

    1986-01-01

    Presents an activity, suitable for students in grades 6-12, on generating random numbers. Objectives, equipment needed, list of prerequisite experiences, instructional strategies, and ready-to-copy student worksheets are included. (JN)

  12. Social Security Number (SSN) Verification

    Data.gov (United States)

    U.S. Department of Health & Human Services — This report presents the results of a validation study of Social Security numbers (SSNs) in Medicaid Statistical Information System (MSIS) records for the fourth...

  13. Subject-verb number (disagreement

    Directory of Open Access Journals (Sweden)

    Daniela Isac

    2010-01-01

    Full Text Available This paper discusses cases of number mismatches between subjects and verbs. The main proposal is that subject-verb agreement is not in number but in a different feature, that we call Cardinality. Cardinality is a feature of DPs that is computed on the basis of number features and collectivity features carried by various heads in the DP. The “computation” of the Cardinality feature proceeds internal to the feature matrix of one lexical item - the D. The values of the number and collectivity features carried by various heads in the DP are transferred to the D by means of a feature checking mechanism and the value of the Cardinality feature is then derived from these.

  14. Numbers for reducible cubic scrolls

    Directory of Open Access Journals (Sweden)

    Israel Vainsencher

    2004-12-01

    Full Text Available We show how to compute the number of reducible cubic scrolls of codimension 2 in (math blackboard symbol Pn incident to the appropriate number of linear spaces.Mostramos como calcular o número de rolos cúbicos redutíveis de codimensão 2 em (math blackboard symbol Pn incidentes a espaços lineares apropriados.

  15. Digital random-number generator

    Science.gov (United States)

    Brocker, D. H.

    1973-01-01

    For binary digit array of N bits, use N noise sources to feed N nonlinear operators; each flip-flop in digit array is set by nonlinear operator to reflect whether amplitude of generator which feeds it is above or below mean value of generated noise. Fixed-point uniform distribution random number generation method can also be used to generate random numbers with other than uniform distribution.

  16. Random numbers from vacuum fluctuations

    International Nuclear Information System (INIS)

    Shi, Yicheng; Kurtsiefer, Christian; Chng, Brenda

    2016-01-01

    We implement a quantum random number generator based on a balanced homodyne measurement of vacuum fluctuations of the electromagnetic field. The digitized signal is directly processed with a fast randomness extraction scheme based on a linear feedback shift register. The random bit stream is continuously read in a computer at a rate of about 480 Mbit/s and passes an extended test suite for random numbers.

  17. Banner prints social security numbers

    OpenAIRE

    Robbins RA

    2014-01-01

    No abstract available. Article truncated at 150 words. The Monday edition of the Arizona Republic contained a story with potential interest to our readers. On the most recent address labels of Banner Health's magazine, Smart & Healthy, the addressee's Social Security or Medicare identification numbers, which are often identical to their Social Security numbers (1). The magazine was mailed to more than 50,000 recipients in Arizona late last week. The recipients are members of the Medicare Pion...

  18. Unit Monitors Manchester-Format Data Buses

    Science.gov (United States)

    Amador, Jose J.

    1994-01-01

    Circuit card converts data signals into convenient hexadecimal form for troubleshooting. Bus-monitoring unit converts data signals from Manchester II format used on data bus into hexadecimal format. Monitoring circuit causes hexadecimal words to display on video terminal, where test engineer compares them with hexadecimal records for troubleshooting. Circuit monitors one bus or two buses simultaneously.

  19. From Natural Numbers to Numbers and Curves in Nature - II

    Indian Academy of Sciences (India)

    sunflowers have 34, 55 or 89 petals. If one carefully observes the row of scales on the surface of a pineapple, then these diamond shaped marks are seen to follow two spirals sloping in opposite directions. It is found that the helix angles of these two spirals are different. If one counts the numbers of these marks along these.

  20. Are Number Gestures Easier than Number Words for Preschoolers?

    Science.gov (United States)

    Nicoladis, Elena; Pika, Simone; Marentette, Paula

    2010-01-01

    Some researchers have argued that children's earliest symbols are based on their sensorimotor experience and that arbitrary symbol-referent mapping poses a challenge for them. If so, exposure to iconic symbols (such as one-finger-for-one-object manual gestures) might help children in a difficult domain such as number. We assessed 44 preschoolers'…

  1. Number Meaning and Number Grammar in English and Spanish

    Science.gov (United States)

    Bock, Kathryn; Carreiras, Manuel; Meseguer, Enrique

    2012-01-01

    Grammatical agreement makes different demands on speakers of different languages. Being widespread in the languages of the world, the features of agreement systems offer valuable tests of how language affects deep-seated domains of human cognition and categorization. Number agreement is one such domain, with intriguing evidence that typological…

  2. Searching for the highest number.

    Science.gov (United States)

    Howe, Piers D L; Little, Daniel R

    2015-02-01

    When viewing a collection of products how does a consumer decide which one to buy? To do this task, the consumer not only needs to evaluate the desirability of the products, taking into account factors such as quality and price, but also needs to search through the products to find the most desirable one. We studied the search process using an abstraction of a common consumer choice task. In our task, observers searched an array of numbers for the highest. Crucially, the observers did not know in advance what this number would be, which made it difficult to know when the search should be terminated. In this way, our search task mimicked a problem often faced by consumers in a supermarket setting where they also may not know in advance what the most desirable product will be. We compared several computational models. We found that our data was best described by a process that assumes that observers terminate their search when they find a number that exceeds an internal threshold. Depending on the observer and the circumstances, this threshold appeared either to be fixed or to decrease over the course of the trial. This threshold can explain why in some situations the observers terminate the search without inspecting all the numbers in the display, whereas in other situations observers act in a seemingly irrational manner, continuing the search even after inspecting all the numbers.

  3. The MIXMAX random number generator

    Science.gov (United States)

    Savvidy, Konstantin G.

    2015-11-01

    In this paper, we study the randomness properties of unimodular matrix random number generators. Under well-known conditions, these discrete-time dynamical systems have the highly desirable K-mixing properties which guarantee high quality random numbers. It is found that some widely used random number generators have poor Kolmogorov entropy and consequently fail in empirical tests of randomness. These tests show that the lowest acceptable value of the Kolmogorov entropy is around 50. Next, we provide a solution to the problem of determining the maximal period of unimodular matrix generators of pseudo-random numbers. We formulate the necessary and sufficient condition to attain the maximum period and present a family of specific generators in the MIXMAX family with superior performance and excellent statistical properties. Finally, we construct three efficient algorithms for operations with the MIXMAX matrix which is a multi-dimensional generalization of the famous cat-map. First, allowing to compute the multiplication by the MIXMAX matrix with O(N) operations. Second, to recursively compute its characteristic polynomial with O(N2) operations, and third, to apply skips of large number of steps S to the sequence in O(N2 log(S)) operations.

  4. Experimental determination of Ramsey numbers.

    Science.gov (United States)

    Bian, Zhengbing; Chudak, Fabian; Macready, William G; Clark, Lane; Gaitan, Frank

    2013-09-27

    Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers R(m,n). Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(m,2) for 4≤m≤8. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.

  5. Sequences, groups, and number theory

    CERN Document Server

    Rigo, Michel

    2018-01-01

    This collaborative book presents recent trends on the study of sequences, including combinatorics on words and symbolic dynamics, and new interdisciplinary links to group theory and number theory. Other chapters branch out from those areas into subfields of theoretical computer science, such as complexity theory and theory of automata. The book is built around four general themes: number theory and sequences, word combinatorics, normal numbers, and group theory. Those topics are rounded out by investigations into automatic and regular sequences, tilings and theory of computation, discrete dynamical systems, ergodic theory, numeration systems, automaton semigroups, and amenable groups.  This volume is intended for use by graduate students or research mathematicians, as well as computer scientists who are working in automata theory and formal language theory. With its organization around unified themes, it would also be appropriate as a supplemental text for graduate level courses.

  6. Magic Numbers in Protein Structures

    DEFF Research Database (Denmark)

    Lindgård, Per-Anker; Bohr, Henrik

    1996-01-01

    A homology measure for protein fold classes has been constructed by locally projecting consecutive secondary structures onto a lattice. Taking into account hydrophobic forces we have found a mechanism for formation of domains containing magic numbers of secondary structures and multipla of these ......A homology measure for protein fold classes has been constructed by locally projecting consecutive secondary structures onto a lattice. Taking into account hydrophobic forces we have found a mechanism for formation of domains containing magic numbers of secondary structures and multipla...

  7. Lenstra theorem in number fields

    Indian Academy of Sciences (India)

    Indian Acad. Sci. (Math. Sci.) Vol. 124, No. 4, November 2014, pp. 481– 485. c Indian Academy of Sciences. Lenstra theorem in number fields. S SUBBURAM. Department of Mathematics, SASTRA University, Thanjavur 613 401, India. Present Address: The Institute of Mathematics, CIT Campus, Taramani,. Chennai 600 113 ...

  8. The elephant brain in numbers

    Science.gov (United States)

    Herculano-Houzel, Suzana; Avelino-de-Souza, Kamilla; Neves, Kleber; Porfírio, Jairo; Messeder, Débora; Mattos Feijó, Larissa; Maldonado, José; Manger, Paul R.

    2014-01-01

    What explains the superior cognitive abilities of the human brain compared to other, larger brains? Here we investigate the possibility that the human brain has a larger number of neurons than even larger brains by determining the cellular composition of the brain of the African elephant. We find that the African elephant brain, which is about three times larger than the human brain, contains 257 billion (109) neurons, three times more than the average human brain; however, 97.5% of the neurons in the elephant brain (251 billion) are found in the cerebellum. This makes the elephant an outlier in regard to the number of cerebellar neurons compared to other mammals, which might be related to sensorimotor specializations. In contrast, the elephant cerebral cortex, which has twice the mass of the human cerebral cortex, holds only 5.6 billion neurons, about one third of the number of neurons found in the human cerebral cortex. This finding supports the hypothesis that the larger absolute number of neurons in the human cerebral cortex (but not in the whole brain) is correlated with the superior cognitive abilities of humans compared to elephants and other large-brained mammals. PMID:24971054

  9. Strouhal number for free swimming

    Science.gov (United States)

    Saadat, Mehdi; van Buren, Tyler; Floryan, Daniel; Smits, Alexander; Haj-Hariri, Hossein

    2015-11-01

    In this work, we present experimental results to explore the implications of free swimming for Strouhal number (as an outcome) in the context of a simple model for a fish that consists of a 2D virtual body (source of drag) and a 2D pitching foil (source of thrust) representing cruising with thunniform locomotion. The results validate the findings of Saadat and Haj-Hariri (2012): for pitching foils thrust coefficient is a function of Strouhal number for all gaits having amplitude less than a certain critical value. Equivalently, given the balance of thrust and drag forces at cruise, Strouhal number is only a function of the shape, i.e. drag coefficient and area, and essentially a constant for high enough swimming speeds for which the mild dependence of drag coefficient on the speed vanishes. Furthermore, a dimensional analysis generalizes the findings. A scaling analysis shows that the variation of Strouhal number with cruising speed is functionally related to the variation of body drag coefficient with speed. Supported by ONR MURI Grant N00014-14-1-0533.

  10. A generalized sense of number.

    Science.gov (United States)

    Arrighi, Roberto; Togoli, Irene; Burr, David C

    2014-12-22

    Much evidence has accumulated to suggest that many animals, including young human infants, possess an abstract sense of approximate quantity, a number sense. Most research has concentrated on apparent numerosity of spatial arrays of dots or other objects, but a truly abstract sense of number should be capable of encoding the numerosity of any set of discrete elements, however displayed and in whatever sensory modality. Here, we use the psychophysical technique of adaptation to study the sense of number for serially presented items. We show that numerosity of both auditory and visual sequences is greatly affected by prior adaptation to slow or rapid sequences of events. The adaptation to visual stimuli was spatially selective (in external, not retinal coordinates), pointing to a sensory rather than cognitive process. However, adaptation generalized across modalities, from auditory to visual and vice versa. Adaptation also generalized across formats: adapting to sequential streams of flashes affected the perceived numerosity of spatial arrays. All these results point to a perceptual system that transcends vision and audition to encode an abstract sense of number in space and in time.

  11. Linking numbers and variational method

    International Nuclear Information System (INIS)

    Oda, I.; Yahikozawa, S.

    1989-09-01

    The ordinary and generalized linking numbers for two surfaces of dimension p and n-p-1 in an n dimensional manifold are derived. We use a variational method based on the properties of topological quantum field theory in order to derive them. (author). 13 refs, 2 figs

  12. RELATIONSHIP BETWEEN SLUDGE DEWATERABILITY NUMBER ...

    African Journals Online (AJOL)

    A representative of a sludge sample collected from the same source was filtered under the same environmental condition and the result analysed with two different concepts. One method of analysis uses Sludge Dewaterability Number, while the second employed the Carman's Specific resistance concept in sludge ...

  13. On badly approximable complex numbers

    DEFF Research Database (Denmark)

    Esdahl-Schou, Rune; Kristensen, S.

    We show that the set of complex numbers which are badly approximable by ratios of elements of , where has maximal Hausdorff dimension. In addition, the intersection of these sets is shown to have maximal dimension. The results remain true when the sets in question are intersected with a suitably...

  14. Number theory via Representation theory

    Indian Academy of Sciences (India)

    2014-11-09

    Nov 9, 2014 ... What is known? The answer depends on two quantities: 1. The weight k of f , which is a positive integer ≥ 2. 2. The slope v of f , a positive (rational) number which. (roughly) measures how divisible ap is by p.

  15. An introduction to Catalan numbers

    CERN Document Server

    Roman, Steven

    2015-01-01

    This textbook provides an introduction to the Catalan numbers and their remarkable properties, along with their various applications in combinatorics.  Intended to be accessible to students new to the subject, the book begins with more elementary topics before progressing to more mathematically sophisticated topics.  Each chapter focuses on a specific combinatorial object counted by these numbers, including paths, trees, tilings of a staircase, null sums in Zn+1, interval structures, partitions, permutations, semiorders, and more.  Exercises are included at the end of book, along with hints and solutions, to help students obtain a better grasp of the material.  The text is ideal for undergraduate students studying combinatorics, but will also appeal to anyone with a mathematical background who has an interest in learning about the Catalan numbers. “Roman does an admirable job of providing an introduction to Catalan numbers of a different nature from the previous ones.  He has made an excellent choice o...

  16. World Epidemiology Review, Number 91

    Science.gov (United States)

    1978-02-09

    consequent continuation of the prophylactic vaccination against diphtheria, whoop- ing cough, tetanus, tuberculosis , infantile paralysis and measles...measles, tetanus and infantile tuberculosis . At least 10 million remain physically handicapped. NUMBER OF PHYSICIANS, DENTISTS TO INCREASE East Berlin...general activity in this sphere be further expanded and that deadly diseases such as tuberculosis , typhus, poliomyelitis, and others, be brought under

  17. Materiales. Numbers 17-20.

    Science.gov (United States)

    Materiales, 1995

    1995-01-01

    Four booklets present articles on Spanish language and culture aimed at teachers of Spanish in the United States for student use in their classes. Number 17, "Los Jovenes Espanoles" (Spanish Youth), includes articles on Spanish youth sports, music, gangs, thoughts, and t-shirt slogans: (1) "Young Spanish Athletes"; (2)…

  18. Materiales. Numbers 21-23.

    Science.gov (United States)

    Materiales, 1997

    1997-01-01

    These three journals of contemporary cultural, historical, and social interest contain activities designed to enhance the awareness of students of Spanish as a foreign language regarding the entire panorama of daily life in Spain. Number 21 focuses on the role of modern Spanish women; their career status; female authors; and the changing place of…

  19. Complex Numbers and Plane Geometry

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 13; Issue 1. Complex Numbers and Plane Geometry. Anant R Shastri. General Article Volume 13 Issue 1 January 2008 pp 35-53. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/013/01/0035-0053. Keywords.

  20. Counting problems for number rings

    NARCIS (Netherlands)

    Brakenhoff, Johannes Franciscus

    2009-01-01

    In this thesis we look at three counting problems connected to orders in number fields. First we study the probability that for a random polynomial f in Z[X] the ring Z[X]/f is the maximal order in Q[X]/f. Connected to this is the probability that a random polynomial has a squarefree

  1. Determination model for cetane number of biodiesel at different fatty acid composition: a review

    Directory of Open Access Journals (Sweden)

    Michal Angelovič

    2014-05-01

    Full Text Available The most accepted definition of biodiesel is stated at the EU technical regulation EN 14214 (2008 or in the USA in ASTM 6751-02. As a result of this highly strict description only methyl esters of fatty acids conform to these definitions, nevertheless the term ‘‘biodiesel’’ is spread out to other alkyl fatty esters. Some countries have adopted bioethanol for replacement of methanol in biodiesel transesterification and thus assuring a fully biological fuel. Of course, such position brings some problems in fulfilling technical requirements of EN 14214 or ASTM 6751-02. Biodiesel is actually a less complex mixture than petrodiesel, but different feedstock origins and the effect of seasonality may impose difficulties in fuel quality control. Since biodiesel is an alternative diesel fuel derived from the transesterification of triacylglycerol comprised materials, such as vegetable oils or animal fats, with simple alcohols to furnish the corresponding mono-alkyl esters, its composition depends on the raw material used, the cultivated area location, and harvest time. The choice of the raw material is usually the most important factor for fluctuations of biodiesel composition, because different vegetable oils and animal fats may contain different types of fatty acids. Important properties of this fuel vary significantly with the composition of the mixture. Cetane number, melting point, degree of saturation, density, cloud point, pour point, viscosity, and nitrogen oxides exhaust emission (NOx, for instance, deserve to be mentioned. One of the most important fuel quality indicators is the cetane number; however its experimental determination may be an expensive and lengthy task. To weaken situation concerning biodiesel, the availability of data in the literature is also scarce. In such scenario, the use of reliable models to predict the cetane number or any other essential characteristic may be of great utility. We reviewed available literature to

  2. Intersection numbers of spectral curves

    CERN Document Server

    Eynard, B

    2011-01-01

    We compute the symplectic invariants of an arbitrary spectral curve with only 1 branchpoint in terms of integrals of characteristic classes in the moduli space of curves. Our formula associates to any spectral curve, a characteristic class, which is determined by the laplace transform of the spectral curve. This is a hint to the key role of Laplace transform in mirror symmetry. When the spectral curve is y=\\sqrt{x}, the formula gives Kontsevich--Witten intersection numbers, when the spectral curve is chosen to be the Lambert function \\exp{x}=y\\exp{-y}, the formula gives the ELSV formula for Hurwitz numbers, and when one chooses the mirror of C^3 with framing f, i.e. \\exp{-x}=\\exp{-yf}(1-\\exp{-y}), the formula gives the topological vertex formula, i.e. the generating function of Gromov-Witten invariants of C^3. In some sense this formula generalizes ELSV formula, and Mumford formula.

  3. Gaussian distribution of LMOV numbers

    Directory of Open Access Journals (Sweden)

    A. Mironov

    2017-11-01

    Full Text Available Recent advances in knot polynomial calculus allowed us to obtain a huge variety of LMOV integers counting degeneracy of the BPS spectrum of topological theories on the resolved conifold and appearing in the genus expansion of the plethystic logarithm of the Ooguri–Vafa partition functions. Already the very first look at this data reveals that the LMOV numbers are randomly distributed in genus (! and are very well parameterized by just three parameters depending on the representation, an integer and the knot. We present an accurate formulation and evidence in support of this new puzzling observation about the old puzzling quantities. It probably implies that the BPS states, counted by the LMOV numbers can actually be composites made from some still more elementary objects.

  4. Gaussian distribution of LMOV numbers

    Science.gov (United States)

    Mironov, A.; Morozov, A.; Morozov, An.; Sleptsov, A.

    2017-11-01

    Recent advances in knot polynomial calculus allowed us to obtain a huge variety of LMOV integers counting degeneracy of the BPS spectrum of topological theories on the resolved conifold and appearing in the genus expansion of the plethystic logarithm of the Ooguri-Vafa partition functions. Already the very first look at this data reveals that the LMOV numbers are randomly distributed in genus (!) and are very well parameterized by just three parameters depending on the representation, an integer and the knot. We present an accurate formulation and evidence in support of this new puzzling observation about the old puzzling quantities. It probably implies that the BPS states, counted by the LMOV numbers can actually be composites made from some still more elementary objects.

  5. Generalized r-Lah numbers

    Indian Academy of Sciences (India)

    themselves the smallest element of a block. Let nrec(λ) denote the number of elements of. [n] which are not record lows of λ. To illustrate, if λ is as above, then rec. ∗. (λ) = 2 (for the 8 and 4) and nrec(λ) = 4 (for. 5, 3, 7 and 9). We now consider the restriction of the rec. ∗ and nrec statistics to Lr(n, k) and define the distribution ...

  6. Number theory meets Higgs physics

    CERN Multimedia

    CERN. Geneva

    2014-01-01

    Inspired by results from modern number theory and algebraic geometry, a lot of progress has recently been made regarding the computation of multi-loop integrals and scattering amplitudes. I will discuss various new approaches to the computation of loop integrals, and illustrate them on the first computation of a quantity at N3LO in perturbative QCD, the soft-virtual part of the inclusive Higgs-boson cross section in gluon fusion at N3LO.

  7. On the number of matroids

    NARCIS (Netherlands)

    N. Bansal (Nikhil); R. Pendavingh; J.G. van der Pol (Jorn)

    2013-01-01

    htmlabstractWe consider the problem of determining mn, the number of matroids on n elements. The best known lower bound on mn is due to Knuth (1974) who showed that log log mn is at least n− 3 2 log n−O(1). On the other hand, Piff (1973) showed that log log mn ≤ n − log n + log log n + O(1),

  8. World Epidemiology Review, Number 105.

    Science.gov (United States)

    1978-09-13

    fruit, beverages, and other food items handled by him are likely to get infected. 37 Fruit and vegetables consumed uncooked, such as lettuce ...pure. Cholera bacteria can remain in the folds of lettuce , carrots, radishes, and similar vegetables even when they are carefully washed. It should...numbers of aphids are due to appear on the alfalfa in the near future. The infestation has approached and even exceeded the extent at which serious

  9. Covering Numbers for Semicontinuous Functions

    Science.gov (United States)

    2016-04-29

    Although a comparison to the classical result of O(ε−d) for Lipschitz continuous functions on bounded subsets, which goes back to [17] (see for...Covering Numbers for Semicontinuous Functions Johannes O. Royset Operations Research Department Naval Postgraduate School joroyset@nps.edu Abstract...Considering the metric space of extended real-valued lower semicontinuous functions under the epi-distance, the paper gives an upper bound on the

  10. Secular Love number of Phobos

    International Nuclear Information System (INIS)

    Bursa, M.

    1988-01-01

    The secular Love number of Phobos was estimated k s =10.4. It only deviates by one order of magnitude from that corresponding to the ideal equilibrium state. It is not in contradiction with the theory of the origin of Phobos as a result of the accretion around Mars. In its early history, the rotation period of Phobos had been estimated to be approx. 2.4 hours. (author). 1 tab., 4 refs

  11. More Sets, Graphs and Numbers

    CERN Document Server

    Gyori, Ervin; Lovasz, Laszlo

    2006-01-01

    This volume honours the eminent mathematicians Vera Sos and Andras Hajnal. The book includes survey articles reviewing classical theorems, as well as new, state-of-the-art results. Also presented are cutting edge expository research papers with new theorems and proofs in the area of the classical Hungarian subjects, like extremal combinatorics, colorings, combinatorial number theory, etc. The open problems and the latest results in the papers are sure to inspire further research.

  12. Approximate number sense, symbolic number processing, or number-space mappings: what underlies mathematics achievement?

    Science.gov (United States)

    Sasanguie, Delphine; Göbel, Silke M; Moll, Kristina; Smets, Karolien; Reynvoet, Bert

    2013-03-01

    In this study, the performance of typically developing 6- to 8-year-old children on an approximate number discrimination task, a symbolic comparison task, and a symbolic and nonsymbolic number line estimation task was examined. For the first time, children's performances on these basic cognitive number processing tasks were explicitly contrasted to investigate which of them is the best predictor of their future mathematical abilities. Math achievement was measured with a timed arithmetic test and with a general curriculum-based math test to address the additional question of whether the predictive association between the basic numerical abilities and mathematics achievement is dependent on which math test is used. Results revealed that performance on both mathematics achievement tests was best predicted by how well childrencompared digits. In addition, an association between performance on the symbolic number line estimation task and math achievement scores for the general curriculum-based math test measuring a broader spectrum of skills was found. Together, these results emphasize the importance of learning experiences with symbols for later math abilities. Copyright © 2012 Elsevier Inc. All rights reserved.

  13. Nielsen number and differential equations

    Directory of Open Access Journals (Sweden)

    Andres Jan

    2005-01-01

    Full Text Available In reply to a problem of Jean Leray (application of the Nielsen theory to differential equations, two main approaches are presented. The first is via Poincaré's translation operator, while the second one is based on the Hammerstein-type solution operator. The applicability of various Nielsen theories is discussed with respect to several sorts of differential equations and inclusions. Links with the Sharkovskii-like theorems (a finite number of periodic solutions imply infinitely many subharmonics are indicated, jointly with some further consequences like the nontrivial -structure of solutions of initial value problems. Some illustrating examples are supplied and open problems are formulated.

  14. On the intriguing number 1001

    DEFF Research Database (Denmark)

    Krarup, Jakob

    2016-01-01

    Born in 1936 I was a schoolboy on the threshold of the secondary school when a knapsack-type game was played with a class mate around 1946–1947. To play the game well and fascinated by numbers in general since my early childhood, however, I realized soon the usefulness of knowing that 1001 = 7 × 11...... × 13. Today, about 70 years later, the game has been passed to some of my grandchildren who also should convince themselves that simple, arithmetic calculations do not necessarily require a pocket computer. As a side effect of the recent revival of the game I felt motivated to seek more insight...

  15. Random number generators and causality

    International Nuclear Information System (INIS)

    Larrondo, H.A.; Martin, M.T.; Gonzalez, C.M.; Plastino, A.; Rosso, O.A.

    2006-01-01

    We advance a prescription to randomize physical or algorithmic Random Number Generators (RNG's) that do not pass Marsaglia's DIEHARD test suite and discuss a special physical quantifier, based on an intensive statistical complexity measure, that is able to adequately assess the improvements produced thereby. Eight RNG's are evaluated and the associated results are compared to those obtained by recourse to Marsaglia's DIEHARD test suite. Our quantifier, which is evaluated using causality arguments, can forecast whether a given RNG will pass the above mentioned test

  16. Propulsion at low Reynolds number

    Energy Technology Data Exchange (ETDEWEB)

    Najafi, Ali [Institute for Advanced Studies in Basic Sciences, Zanjan 45195-159 (Iran, Islamic Republic of); Faculty of Science, Zanjan University, Zanjan 313 (Iran, Islamic Republic of); Golestanian, Ramin [Institute for Advanced Studies in Basic Sciences, Zanjan 45195-159 (Iran, Islamic Republic of)

    2005-04-13

    We study the propulsion of two model swimmers at low Reynolds number. Inspired by Purcell's model, we propose a very simple one-dimensional swimmer consisting of three spheres that are connected by two arms whose lengths can change between two values. The proposed swimmer can swim with a special type of motion, which breaks the time-reversal symmetry. We also show that an ellipsoidal membrane with tangential travelling wave on it can also propel itself in the direction preferred by the travelling wave. This system resembles the realistic biological animals like Paramecium.

  17. Propulsion at low Reynolds number

    International Nuclear Information System (INIS)

    Najafi, Ali; Golestanian, Ramin

    2005-01-01

    We study the propulsion of two model swimmers at low Reynolds number. Inspired by Purcell's model, we propose a very simple one-dimensional swimmer consisting of three spheres that are connected by two arms whose lengths can change between two values. The proposed swimmer can swim with a special type of motion, which breaks the time-reversal symmetry. We also show that an ellipsoidal membrane with tangential travelling wave on it can also propel itself in the direction preferred by the travelling wave. This system resembles the realistic biological animals like Paramecium

  18. Number Theory, Analysis and Geometry

    CERN Document Server

    Goldfeld, Dorian; Jones, Peter

    2012-01-01

    Serge Lang was an iconic figure in mathematics, both for his own important work and for the indelible impact he left on the field of mathematics, on his students, and on his colleagues. Over the course of his career, Lang traversed a tremendous amount of mathematical ground. As he moved from subject to subject, he found analogies that led to important questions in such areas as number theory, arithmetic geometry, and the theory of negatively curved spaces. Lang's conjectures will keep many mathematicians occupied far into the future. In the spirit of Lang's vast contribution to mathematics, th

  19. Number theory III Diophantine geometry

    CERN Document Server

    1991-01-01

    From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics ...

  20. Banner prints social security numbers

    Directory of Open Access Journals (Sweden)

    Robbins RA

    2014-02-01

    Full Text Available No abstract available. Article truncated at 150 words. The Monday edition of the Arizona Republic contained a story with potential interest to our readers. On the most recent address labels of Banner Health's magazine, Smart & Healthy, the addressee's Social Security or Medicare identification numbers, which are often identical to their Social Security numbers (1. The magazine was mailed to more than 50,000 recipients in Arizona late last week. The recipients are members of the Medicare Pioneer Accountable Care Organization, a government health-care plan that Banner serves. Banner generated its mailing list from information it received from the U.S. Centers for Medicare & Medicaid Services, which is an agency within the U.S. Department of Health & Human Services (HHS responsible for administration of several federal health-care programs. Although medical information has been protected by the Health Insurance Portability and Accountability Act (HIPAA since 1996, penalties were recently increased. Civil monetary penalties were increased from a maximum of $100 ...

  1. Topics in Number Theory Conference

    CERN Document Server

    Andrews, George; Ono, Ken

    1999-01-01

    From July 31 through August 3,1997, the Pennsylvania State University hosted the Topics in Number Theory Conference. The conference was organized by Ken Ono and myself. By writing the preface, I am afforded the opportunity to express my gratitude to Ken for beng the inspiring and driving force behind the whole conference. Without his energy, enthusiasm and skill the entire event would never have occurred. We are extremely grateful to the sponsors of the conference: The National Sci­ ence Foundation, The Penn State Conference Center and the Penn State Depart­ ment of Mathematics. The object in this conference was to provide a variety of presentations giving a current picture of recent, significant work in number theory. There were eight plenary lectures: H. Darmon (McGill University), "Non-vanishing of L-functions and their derivatives modulo p. " A. Granville (University of Georgia), "Mean values of multiplicative functions. " C. Pomerance (University of Georgia), "Recent results in primality testing. " C. ...

  2. Cryptography and computational number theory

    CERN Document Server

    Shparlinski, Igor; Wang, Huaxiong; Xing, Chaoping; Workshop on Cryptography and Computational Number Theory, CCNT'99

    2001-01-01

    This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na­ tional University of Singapore. We gratefully acknowledge the financial support from the Singapore National Science and Technology Board under the grant num­ ber RP960668/M. The idea for this workshop grew out of the recognition of the recent, rapid development in various areas of cryptography and computational number the­ ory. The event followed the concept of the research programs at such well-known research institutions as the Newton Institute (UK), Oberwolfach and Dagstuhl (Germany), and Luminy (France). Accordingly, there were only invited lectures at the workshop with plenty of time for informal discussions. It was hoped and successfully achieved that the meeting would encourage and stimulate further research in information and computer s...

  3. Signals of lepton number violation

    CERN Document Server

    Panella, O; Srivastava, Y N

    1999-01-01

    The production of like-sign-dileptons (LSD), in the high energy lepton number violating ( Delta L=+2) reaction, pp to 2jets+l/sup +/l /sup +/, (l=e, mu , tau ), of interest for the experiments to be performed at the forthcoming Large Hadron Collider (LHC), is reported, taking up a composite model scenario in which the exchanged virtual composite neutrino is assumed to be a Majorana particle. Numerical estimates of the corresponding signal cross-section that implement kinematical cuts needed to suppress the standard model background, are presented which show that in some regions of the parameter space the total number of LSD events is well above the background. Assuming non-observation of the LSD signal it is found that LHC would exclude a composite Majorana neutrino up to 700 GeV (if one requires 10 events for discovery). The sensitivity of LHC experiments to the parameter space is then compared to that of the next generation of neutrinoless double beta decay ( beta beta /sub 0 nu /) experiment, GENIUS, and i...

  4. Polynomials formalism of quantum numbers

    International Nuclear Information System (INIS)

    Kazakov, K.V.

    2005-01-01

    Theoretical aspects of the recently suggested perturbation formalism based on the method of quantum number polynomials are considered in the context of the general anharmonicity problem. Using a biatomic molecule by way of example, it is demonstrated how the theory can be extrapolated to the case of vibrational-rotational interactions. As a result, an exact expression for the first coefficient of the Herman-Wallis factor is derived. In addition, the basic notions of the formalism are phenomenologically generalized and expanded to the problem of spin interaction. The concept of magneto-optical anharmonicity is introduced. As a consequence, an exact analogy is drawn with the well-known electro-optical theory of molecules, and a nonlinear dependence of the magnetic dipole moment of the system on the spin and wave variables is established [ru

  5. Galaxy number counts: Pt. 2

    International Nuclear Information System (INIS)

    Metcalfe, N.; Shanks, T.; Fong, R.; Jones, L.R.

    1991-01-01

    Using the Prime Focus CCD Camera at the Isaac Newton Telescope we have determined the form of the B and R galaxy number-magnitude count relations in 12 independent fields for 21 m ccd m and 19 m ccd m 5. The average galaxy count relations lie in the middle of the wide range previously encompassed by photographic data. The field-to-field variation of the counts is small enough to define the faint (B m 5) galaxy count to ±10 per cent and this variation is consistent with that expected from galaxy clustering considerations. Our new data confirm that the B, and also the R, galaxy counts show evidence for strong galaxy luminosity evolution, and that the majority of the evolving galaxies are of moderately blue colour. (author)

  6. Put numbers on the sustainability

    DEFF Research Database (Denmark)

    Hauschild, Michael Zwicky

    2014-01-01

    life cycle Environmental sustainability encompasses multiple types of environmental impact ranging from the global scale like climate change and stratospheric ozone depletion over regional impacts associated with air pollution impacts causing acidification, photochemical ozone formation and particle...... exposure of humans, to the local impacts associated with physical transformation of land and extraction of water. Chemicals can cause toxic impacts to humans and ecosystems on all scales. All these impacts need to be quantified if we want to put numbers on sustainability. The life cycle perspective......Sustainability is about meeting the needs of the present without compromising the possibilities for our future generations to meet their needs and is commonly perceived as comprising three dimensions – a social, an economic and an environmental dimension, e.g. in the triple bottom line thinking...

  7. Effects of non-uniform interfacial tension in small Reynolds number ...

    Indian Academy of Sciences (India)

    We follow the well-established method of solution as devised by Proudman and Pear- son [12] and Taylor and Acrivos [1]. The calculations are lengthy. We shall therefore only present the results and verify that they agree with the established solutions in the appropriate limits. 3. Perturbation solution. The problem is a ...

  8. High Frontier, The Journal for Space & Missile Professionals. Volume 4, Number 4

    Science.gov (United States)

    2008-08-01

    thus advanced space practitioners without the “ scar tissue” neces- sary to manage large procurement activities successfully. To address this growing...is lengthy but includes folks like Lt Gen Mike Hamel, Lt Gen Tom Sheridan, Maj Gen Jimmy Morrell, Maj Gen Jim Armour , Maj Gen Mitch Mitchell, Brig

  9. Fermionic relatives of Stirling and Lah numbers

    International Nuclear Information System (INIS)

    Schork, Matthias

    2003-01-01

    In this paper certain 'fermionic' Stirling numbers introduced recently are discussed. Roughly speaking, these numbers are obtained by taking the 'fermionic' limit q →-1 of the q-deformed Stirling numbers. The usual Stirling numbers correspond in this language to the 'bosonic' limit q → 1. It is shown that the fermionic Stirling numbers are given by binomial coefficients and that they satisfy the same relations as the undeformed Stirling numbers. The fermionic relatives of Lah numbers are also very briefly discussed

  10. Some further results on Legendre numbers

    Directory of Open Access Journals (Sweden)

    Paul W. Haggard

    1988-01-01

    Full Text Available The Legendre numbers, Pnm, are expressed in terms of those numbers, Pkm−1, in the previous column down to Pnm and in terms of those, Pkm, above but in the same column. Other results are given for numbers close to a given number. The limit of the quotient of two consecutive non-zero numbers in any one column is shown to be −1. Bounds for the Legendre numbers are described by circles centered at the origin. A connection between Legendre numbers and Pascal numbers is exhibited by expressing the Legendre numbers in terms of combinations.

  11. IEEE Standard for Floating Point Numbers

    Indian Academy of Sciences (India)

    IAS Admin

    is to decide how to represent real numbers using these bits. Normally, in ... numbers explained above, the largest floating point number which can be represented is. The number of bits to be used for the mantissa is determined by the number of significant decimal .... This is used to give an error message. When an operation.

  12. The magic of a number system

    DEFF Research Database (Denmark)

    Elmasry, Amr Ahmed Abd Elmoneim; Jensen, Claus; Katajainen, Jyrki

    2010-01-01

    We introduce a new number system that supports increments with a constant number of digit changes. We also give a simple method that extends any number system supporting increments to support decrements using the same number of digit changes. In the new number system the weight of the ith digit i...

  13. ON THE BINARY DIGITS OF ALGEBRAIC NUMBERS

    OpenAIRE

    KANEKO, HAJIME

    2010-01-01

    Borel conjectured that all algebraic irrational numbers are normal in base 2. However, very little is known about this problem. We improve the lower bounds for the number of digit changes in the binary expansions of algebraic irrational numbers.

  14. Essays on the theory of numbers

    CERN Document Server

    Dedekind, Richard

    1963-01-01

    Two classic essays by great German mathematician: one provides an arithmetic, rigorous foundation for the irrational numbers, the other is an attempt to give the logical basis for transfinite numbers and properties of the natural numbers.

  15. What Do Numbers Do in Transnational Governance?

    DEFF Research Database (Denmark)

    Krause Hansen, Hans; Porter, Tony

    2012-01-01

    This study examines how numbers in transnational governance constitute actors, objects, and relationships, including relationships of power. We review the existing literatures on numbers for insights relevant to their role in transnational governance, including the ontology of numbers, the histor...

  16. How to be Brilliant at Numbers

    CERN Document Server

    Webber, Beryl

    2010-01-01

    How to be Brilliant at Numbers will help students to develop an understanding of numbers, place value, fractions and decimals. They will develop the language of number, and of the relationships between numbers. They will also use mathematics to solve problems and will develop mathematical reasoning. Using the worksheets in this book, pupils will learn about: ancient Greek numbers; coins; digits; consecutive numbers; magic ladders; fractions; matching pairs; multiples of 10; rounding; decimal un

  17. Number sense in teaching and learning arithmetic

    DEFF Research Database (Denmark)

    Rezat, Sebastian; Ejersbo, Lisser Rye

    2018-01-01

    From the beginning of CERME conferences, the concept of number sense and its relation to the teaching and learning arithmetic and number systems has been a central theme. However, different meanings of the term have been used, and it has not always been clear which meaning is referred to. Depending......? Second, what can be done to foster the development of number sense? Third, what is the scope of number sense in terms of different number domains including fractions and negative numbers?...

  18. The Quest for Pi

    Science.gov (United States)

    Bailey, David H.; Borwein, Jonathan M.; Borwein, Peter B.; Plouffe, Simon

    1996-01-01

    This article gives a brief history of the analysis and computation of the mathematical constant Pi=3.14159 ..., including a number of the formulas that have been used to compute Pi through the ages. Recent developments in this area are then discussed in some detail, including the recent computation of Pi to over six billion decimal digits using high-order convergent algorithms, and a newly discovered scheme that permits arbitrary individual hexadecimal digits of Pi to be computed.

  19. 7 CFR 987.102 - Lot number.

    Science.gov (United States)

    2010-01-01

    ... 7 Agriculture 8 2010-01-01 2010-01-01 false Lot number. 987.102 Section 987.102 Agriculture... RIVERSIDE COUNTY, CALIFORNIA Administrative Rules Definitions § 987.102 Lot number. Lot number is synonymous... letters or numbers, or both, imprinted on the containers shall differ from those of any other lot coded...

  20. Visuospatial Priming of the Mental Number Line

    Science.gov (United States)

    Stoianov, Ivilin; Kramer, Peter; Umilta, Carlo; Zorzi, Marco

    2008-01-01

    It has been argued that numbers are spatially organized along a "mental number line" that facilitates left-hand responses to small numbers, and right-hand responses to large numbers. We hypothesized that whenever the representations of visual and numerical space are concurrently activated, interactions can occur between them, before response…

  1. The Decimal Number System and Young Children

    Science.gov (United States)

    Harrison, John

    2006-01-01

    In this article, the author believes that a visual image of the number system is helpful to everyone, especially children, in understanding what is, after all, an abstract idea. The simplest model is the number line, a row of equally spaced numbers, starting at zero. This illustrates the continuous progression of the natural numbers, moving to the…

  2. Stirling numbers and integer partitions | Merca | Quaestiones ...

    African Journals Online (AJOL)

    In this paper, we prove that the Stirling numbers of both kinds can be written as sums over integer partitions. As corollaries, we rewrite some identities with Stirling numbers of both kinds without Stirling numbers. Keywords: Integer partitions, symmetric functions, Stirling numbers ...

  3. On domination multisubdivision number of unicyclic graphs

    Directory of Open Access Journals (Sweden)

    Joanna Raczek

    2018-01-01

    Full Text Available The paper continues the interesting study of the domination subdivision number and the domination multisubdivision number. On the basis of the constructive characterization of the trees with the domination subdivision number equal to 3 given in [H. Aram, S.M. Sheikholeslami, O. Favaron, Domination subdivision number of trees, Discrete Math. 309 (2009, 622-628], we constructively characterize all connected unicyclic graphs with the domination multisubdivision number equal to 3. We end with further questions and open problems.

  4. Deafness for the meanings of number words

    OpenAIRE

    Caño, Agnès; Rapp, Brenda; Costa, Albert; Juncadella, Montserrat

    2007-01-01

    We describe the performance of an aphasic individual who showed a selective impairment affecting his comprehension of auditorily presented number words and not other word categories. His difficulty in number word comprehension was restricted to the auditory modality, given that with visual stimuli (written words, Arabic numerals and pictures) his comprehension of number and non-number words was intact. While there have been previous reports of selective difficulty or sparing of number words a...

  5. Fast integration using quasi-random numbers

    International Nuclear Information System (INIS)

    Bossert, J.; Feindt, M.; Kerzel, U.

    2006-01-01

    Quasi-random numbers are specially constructed series of numbers optimised to evenly sample a given s-dimensional volume. Using quasi-random numbers in numerical integration converges faster with a higher accuracy compared to the case of pseudo-random numbers. The basic properties of quasi-random numbers are introduced, various generators are discussed and the achieved gain is illustrated by examples

  6. Fast integration using quasi-random numbers

    Science.gov (United States)

    Bossert, J.; Feindt, M.; Kerzel, U.

    2006-04-01

    Quasi-random numbers are specially constructed series of numbers optimised to evenly sample a given s-dimensional volume. Using quasi-random numbers in numerical integration converges faster with a higher accuracy compared to the case of pseudo-random numbers. The basic properties of quasi-random numbers are introduced, various generators are discussed and the achieved gain is illustrated by examples.

  7. Group Sunspot Numbers: Sunspot Cycle Characteristics

    Science.gov (United States)

    Hathaway, D. H.; Wilson, R. M.; Reichmann, E. J.; Six, N. Frank (Technical Monitor)

    2002-01-01

    We examine the "Group" sunspot numbers constructed by Hoyt and Schatten to determine their utility in characterizing the solar activity cycle. We compare smoothed monthly Group Sunspot Numbers to Zurich (International) Sunspot Numbers, 10.7-cm radio flux, and total sunspot area. We find that the Zurich numbers follow the 10.7-cm radio flux and total sunspot area measurements slightly better than the Group numbers. We examine several significant characteristics of the sunspot cycle using both Group numbers and Zurich numbers. We find that the "Waldmeier Effect" - the anti-correlation between cycle amplitude and the elapsed time between minimum and maximum of a cycle - is much more apparent in the Zurich numbers. The "Amplitude-Period Effect" the anti-correlation between cycle amplitude and the length of the previous cycle from minimum to minimum - is also much more apparent in the Zurich numbers. The "Amplitude-Minimum Effect" - the correlation between cycle amplitude and the activity level at the previous (onset) minimum is equally apparent in both the Zurich numbers and the Group numbers. The "Even-Odd Effect" - in which odd-numbered cycles are larger than their even-numbered precursors - is somewhat stronger in the Group numbers but with a tighter relationship in the Zurich numbers. The "Secular Trend" - the increase in cycle amplitudes since the Maunder Minimum - is much stronger in Group numbers. After removing this trend we find little evidence for multi-cycle periodicities like the 80 year Gleissberg cycle or the two- and three-cycle periodicities. We also find little evidence for a correlation between the amplitude of a cycle and its period or for a bimodal distribution of cycle periods. We conclude that the Group numbers are most useful for extending the sunspot cycle data further back in time and thereby adding more cycles and improving the statistics. However, the Zurich numbers are more useful for characterizing the on-going levels of solar activity.

  8. The Translated Dowling Polynomials and Numbers.

    Science.gov (United States)

    Mangontarum, Mahid M; Macodi-Ringia, Amila P; Abdulcarim, Normalah S

    2014-01-01

    More properties for the translated Whitney numbers of the second kind such as horizontal generating function, explicit formula, and exponential generating function are proposed. Using the translated Whitney numbers of the second kind, we will define the translated Dowling polynomials and numbers. Basic properties such as exponential generating functions and explicit formula for the translated Dowling polynomials and numbers are obtained. Convexity, integral representation, and other interesting identities are also investigated and presented. We show that the properties obtained are generalizations of some of the known results involving the classical Bell polynomials and numbers. Lastly, we established the Hankel transform of the translated Dowling numbers.

  9. Observing Optional Number in DDC Edition 23

    Directory of Open Access Journals (Sweden)

    Rotmianto Mohamad

    2018-01-01

    Full Text Available Dewey Decimal Classification is a most popular classification system in the world because of its completeness and most up-to-date. There are many optional number in this classification system, although it rarely to be discussed even it is important to known well about that optional number, especially for a librarian as classifier. This paper is a literature study about Dewey Decimal Classification Edition 23, to describe about optional numbers, particularly the number in relationship with Indonesia’s subject and discipline. This paper is to avoid misunderstanding in interpreted about optional number among librarians, especially for who that does not understand well about optional numbers.

  10. Portrait of a lengthy vaccination trajectory in Burkina Faso: from cultural acceptance of vaccines to actual immunization.

    Science.gov (United States)

    Dugas, Marylène; Dubé, Eric; Kouyaté, Bocar; Sanou, Aboubakary; Bibeau, Gilles

    2009-10-14

    The global recognition of vaccination is strongly related to the fact that it has proved in the past able to dramatically reduce the incidence of certain diseases. Nevertheless, reactions regarding the practice of vaccination still vary among communities, affecting the worldwide vaccination coverage. Numerous studies, conducted from varying perspectives, have focused on explaining this active refusal or resistance to vaccination. Although in some cases low immunization coverage has been well explained by active refusal or resistance to vaccination, little is known about the reasons for low coverage where those reactions are absent or play a minor role, especially outside an epidemic context. This study attempts to explain this situation, which is found in the health district of Nouna in Burkina Faso. An in-depth ethnographic study was undertaken in the health district of Nouna in an effort to understand, from an anthropological point of view, the logic behind the parental decision-making process regarding the vaccination or non-vaccination of children, in a context where rejection of, and reservations concerning vaccination are not major obstacles. Three elements emerged from the analysis: the empirical conceptions of childhood diseases, the perceived efficacy of vaccine and the knowledge of appropriate age for vaccination uptake; the gap between the decision-making process and the actual achievement of vaccination; and the vaccination procedure leading to vaccination uptake in the particular context of the health district of Nouna. The procedures parents must follow in order to obtain vaccination for their children appear complex and constraining, and on certain points discord with the traditional systems of meaning and idioms of distress related to pregnancy, the prevention of childhood diseases and with the cultural matrix shaping decision-making and behaviour. Attention needs to be directed at certain promotional, logistical and structural elements, and at the procedure that must currently be followed to obtain vaccination for a child during routine vaccination sessions, which are currently limiting the active demand for vaccination. ABSTRACT IN FRENCH : See the full article online for a translation of this abstract in French.

  11. Power sum identities with generalized Stirling numbers

    OpenAIRE

    Boyadzhiev, Khristo N.

    2009-01-01

    Several combinatorial identities are presented, involving Stirling functions of the second kind with a complex variable. The identities involve also Stirling numbers of the first kind, binomial coefficients and harmonic numbers.

  12. Number Systems. Popular Lectures in Mathematics.

    Science.gov (United States)

    Fomin, S. V.

    The origin, properties, and applications of various number systems are discussed. Among the 15 topics discussed are: tests for divisibility, the binary system, the game of Nim, computers, and infinite number representations. (MK)

  13. Caspar Wessel on representing complex numbers (1799)

    DEFF Research Database (Denmark)

    Branner, Bodil

    1999-01-01

    In celebration of the bicentenary of the publication of Wessel's paper on the geometric interpretation of complex numbers it is decsribed how Wessel used complex numbers to represent directions in surveying, at least as early as 1787.......In celebration of the bicentenary of the publication of Wessel's paper on the geometric interpretation of complex numbers it is decsribed how Wessel used complex numbers to represent directions in surveying, at least as early as 1787....

  14. Relativistic theory of tidal Love numbers

    OpenAIRE

    Binnington, Taylor; Poisson, Eric

    2009-01-01

    In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neut...

  15. Evaluating Number Sense in Workforce Students

    Science.gov (United States)

    Steinke, Dorothea A.

    2015-01-01

    Earlier institution-sponsored research revealed that about 20% of students in community college basic math and pre-algebra programs lacked a sense of part-whole relationships with whole numbers. Using the same tool with a group of 86 workforce students, about 75% placed five whole numbers on an empty number line in a way that indicated lack of…

  16. Thermal convection for large Prandtl numbers

    NARCIS (Netherlands)

    Grossmann, Siegfried; Lohse, Detlef

    2001-01-01

    The Rayleigh-Bénard theory by Grossmann and Lohse [J. Fluid Mech. 407, 27 (2000)] is extended towards very large Prandtl numbers Pr. The Nusselt number Nu is found here to be independent of Pr. However, for fixed Rayleigh numbers Ra a maximum in the Nu(Pr) dependence is predicted. We moreover offer

  17. On double Hurwitz numbers with completed cycles

    NARCIS (Netherlands)

    Shadrin, S.; Spitz, L.; Zvonkine, D.

    2012-01-01

    In this paper, we collect a number of facts about double Hurwitz numbers, where the simple branch points are replaced by their more general analogues: completed (r + 1)-cycles. In particular, we give a geometric interpretation of these generalized Hurwitz numbers and derive a cut-and-join operator

  18. On the interpretation of number and classifiers

    NARCIS (Netherlands)

    Cheng, L.L.; Doetjes, J.S.; Sybesma, R.P.E.; Zamparelli, R.

    2012-01-01

    Mandarin and Cantonese, both of which are numeral classifier languages, present an interesting puzzle concerning a compositional account of number in the various forms of nominals. First, bare nouns are number neutral (or vague in number). Second, cl-noun combinations appear to have different

  19. Graphing Powers and Roots of Complex Numbers.

    Science.gov (United States)

    Embse, Charles Vonder

    1993-01-01

    Using De Moivre's theorem and a parametric graphing utility, examines powers and roots of complex numbers and allows students to establish connections between the visual and numerical representations of complex numbers. Provides a program to numerically verify the roots of complex numbers. (MDH)

  20. 48 CFR 304.7001 - Numbering acquisitions.

    Science.gov (United States)

    2010-10-01

    ... 48 Federal Acquisition Regulations System 4 2010-10-01 2010-10-01 false Numbering acquisitions. 304.7001 Section 304.7001 Federal Acquisition Regulations System HEALTH AND HUMAN SERVICES GENERAL ADMINISTRATIVE MATTERS Acquisition Instrument Identification Numbering System 304.7001 Numbering acquisitions. (a...

  1. Developmental Changes in the Whole Number Bias

    Science.gov (United States)

    Braithwaite, David W.; Siegler, Robert S.

    2018-01-01

    Many students' knowledge of fractions is adversely affected by whole number bias, the tendency to focus on the separate whole number components (numerator and denominator) of a fraction rather than on the fraction's magnitude (ratio of numerator to denominator). Although whole number bias appears early in the fraction learning process and under…

  2. 7 CFR 29.32 - Identification number.

    Science.gov (United States)

    2010-01-01

    ... 7 Agriculture 2 2010-01-01 2010-01-01 false Identification number. 29.32 Section 29.32 Agriculture Regulations of the Department of Agriculture AGRICULTURAL MARKETING SERVICE (Standards, Inspections, Marketing... INSPECTION Regulations Definitions § 29.32 Identification number. A number or a combination of letters and...

  3. An Introduction to Conway's Games and Numbers

    OpenAIRE

    Schleicher, Dierk; Stoll, Michael

    2004-01-01

    This is an introduction into John Conway's beautiful Combinatorial Game Theory, providing precise statements and detailed proofs for the fundamental parts of his theory. (1) Combinatorial game theory, (2) the GROUP of games, (3) the FIELD of numbers, (4) ordinal numbers, (5) games and numbers, (6) infinitesimal games, (7) impartial games.

  4. The development of the number field sieve

    CERN Document Server

    Lenstra, Hendrik

    1993-01-01

    The number field sieve is an algorithm for finding the prime factors of large integers. It depends on algebraic number theory. Proposed by John Pollard in 1988, the method was used in 1990 to factor the ninth Fermat number, a 155-digit integer. The algorithm is most suited to numbers of a special form, but there is a promising variant that applies in general. This volume contains six research papers that describe the operation of the number field sieve, from both theoretical and practical perspectives. Pollard's original manuscript is included. In addition, there is an annotated bibliography of directly related literature.

  5. Fibonacci and Catalan Numbers An Introduction

    CERN Document Server

    Grimaldi, Ralph

    2012-01-01

    In this one-of-a-kind book, Ralph Grimaldi uses his extensive experience from the classroom and as a leader of mini-courses to present an accessible, single resource on the topics of Fibonacci Numbers and Catalan Numbers . The book first embarks on a complete treatment of Fibonacci numbers. Starting with a historical background on the topic, the author goes on to present the properties of Fibonacci numbers, a slew of introductory-level examples, and in-depth discussion of related topics including compositions and palindromes; tiling and Fibonacci numbers

  6. An adventurer's guide to number theory

    CERN Document Server

    Friedberg, Richard

    1995-01-01

    In this delightful guide, a noted mathematician and teacher offers a witty, historically oriented introduction to number theory, dealing with properties of numbers and with numbers as abstract concepts. Written for readers with an understanding of arithmetic and beginning algebra, the book presents the classical discoveries of number theory, including the work of Pythagoras, Euclid, Diophantus, Fermat, Euler, Lagrange and Gauss.Unlike many authors, however, Mr. Friedberg encourages students to think about the imaginative, playful qualities of numbers as they consider such subjects as primes

  7. Approximation of complex algebraic numbers by algebraic numbers of bounded degree

    OpenAIRE

    Bugeaud, Yann; Evertse, Jan-Hendrik

    2007-01-01

    We investigate how well complex algebraic numbers can be approximated by algebraic numbers of degree at most n. We also investigate how well complex algebraic numbers can be approximated by algebraic integers of degree at most n+1. It follows from our investigations that for every positive integer n there are complex algebraic numbers of degree larger than n that are better approximable by algebraic numbers of degree at most n than almost all complex numbers. As it turns out, these numbers ar...

  8. Fibonacci number of the tadpole graph

    Directory of Open Access Journals (Sweden)

    Joe DeMaio

    2014-10-01

    Full Text Available In 1982, Prodinger and Tichy defined the Fibonacci number of a graph G to be the number of independent sets of the graph G. They did so since the Fibonacci number of the path graph Pn is the Fibonacci number F(n+2 and the Fibonacci number of the cycle graph Cn is the Lucas number Ln. The tadpole graph Tn,k is the graph created by concatenating Cn and Pk with an edge from any vertex of Cn to a pendant of Pk for integers n=3 and k=0. This paper establishes formulae and identities for the Fibonacci number of the tadpole graph via algebraic and combinatorial methods.

  9. Neocortical glial cell numbers in human brains

    DEFF Research Database (Denmark)

    Pelvig, D.P.; Pakkenberg, H.; Stark, A.K.

    2008-01-01

    and neurons and counting were done in each of the four lobes. The study showed that the different subpopulations of glial cells behave differently as a function of age; the number of oligodendrocytes showed a significant 27% decrease over adult life and a strong correlation to the total number of neurons...... while the total astrocyte number is constant through life; finally males have a 28% higher number of neocortical glial cells and a 19% higher neocortical neuron number than females. The overall total number of neocortical neurons and glial cells was 49.3 billion in females and 65.2 billion in males......, a difference of 24% with a high biological variance. These numbers can serve as reference values in quantitative studies of the human neocortex. (C) 2007 Elsevier Inc. All rights reserved Udgivelsesdato: 2008/11...

  10. An Evaluation of App-Based and Paper-Based Number Lines for Teaching Number Comparison

    Science.gov (United States)

    Weng, Pei-Lin; Bouck, Emily C.

    2016-01-01

    Number comparison is a fundamental skill required for academic and functional mathematics (e.g., time, money, purchasing) for students with disabilities. The most commonly used method to teach number comparison is number lines. Although historically paper number lines are used, app-based number lines may offer greater flexibility. This study…

  11. Object-based neglect in number processing

    Science.gov (United States)

    2013-01-01

    Recent evidence suggests that neglect patients seem to have particular problems representing relatively smaller numbers corresponding to the left part of the mental number line. However, while this indicates space-based neglect for representational number space little is known about whether and - if so - how object-based neglect influences number processing. To evaluate influences of object-based neglect in numerical cognition, a group of neglect patients and two control groups had to compare two-digit numbers to an internally represented standard. Conceptualizing two-digit numbers as objects of which the left part (i.e., the tens digit should be specifically neglected) we were able to evaluate object-based neglect for number magnitude processing. Object-based neglect was indicated by a larger unit-decade compatibility effect actually reflecting impaired processing of the leftward tens digits. Additionally, faster processing of within- as compared to between-decade items provided further evidence suggesting particular difficulties in integrating tens and units into the place-value structure of the Arabic number system. In summary, the present study indicates that, in addition to the spatial representation of number magnitude, also the processing of place-value information of multi-digit numbers seems specifically impaired in neglect patients. PMID:23343126

  12. On the binary expansions of algebraic numbers

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, David H.; Borwein, Jonathan M.; Crandall, Richard E.; Pomerance, Carl

    2003-07-01

    Employing concepts from additive number theory, together with results on binary evaluations and partial series, we establish bounds on the density of 1's in the binary expansions of real algebraic numbers. A central result is that if a real y has algebraic degree D > 1, then the number {number_sign}(|y|, N) of 1-bits in the expansion of |y| through bit position N satisfies {number_sign}(|y|, N) > CN{sup 1/D} for a positive number C (depending on y) and sufficiently large N. This in itself establishes the transcendency of a class of reals {summation}{sub n{ge}0} 1/2{sup f(n)} where the integer-valued function f grows sufficiently fast; say, faster than any fixed power of n. By these methods we re-establish the transcendency of the Kempner--Mahler number {summation}{sub n{ge}0}1/2{sup 2{sup n}}, yet we can also handle numbers with a substantially denser occurrence of 1's. Though the number z = {summation}{sub n{ge}0}1/2{sup n{sup 2}} has too high a 1's density for application of our central result, we are able to invoke some rather intricate number-theoretical analysis and extended computations to reveal aspects of the binary structure of z{sup 2}.

  13. Cortical areas involved in Arabic number reading.

    Science.gov (United States)

    Roux, F-E; Lubrano, V; Lauwers-Cances, V; Giussani, C; Démonet, J-F

    2008-01-15

    Distinct functional pathways for processing words and numbers have been hypothesized from the observation of dissociated impairments of these categories in brain-damaged patients. We aimed to identify the cortical areas involved in Arabic number reading process in patients operated on for various brain lesions. Direct cortical electrostimulation was prospectively used in 60 brain mappings. We used object naming and two reading tasks: alphabetic script (sentences and number words) and Arabic number reading. Cortical areas involved in Arabic number reading were identified according to location, type of interference, and distinctness from areas associated with other language tasks. Arabic number reading was sustained by small cortical areas, often extremely well localized (area (Brodmann area 45), the anterior part of the dominant supramarginal gyrus (Brodmann area 40; p area (Brodmann area 37; p areas.

  14. CT number of the fatty liver

    International Nuclear Information System (INIS)

    Maeda, Hiroko; Kawai, Takeshi; Kanasaki, Yoshiki; Akagi, Hiroaki

    1981-01-01

    This report is studied on CT number and CT images of the eight cases with fatty liver. Five of these cases showed the reversal of densities of the liver and vessels. In these cases, the diagnoses of the fatty liver were easible. In other cases, the diagnoses were possible only by comparison of the CT number of the liver and spleen because the CT number of normal liver were higher than those of the spleen. In the results which we examined the correlation of the CT number and specific gravities of the blood, normal saline, distilled water, mayonnaise, eatable iol, ethyl alcohol and lard, we observed the linear relationship between CT number and specific gravities. And so, we think that the diagnosis of the fatty liver and the degree of fatty infiltration can be guessed by the CT number of the liver and spleen. (author)

  15. Relativistic theory of tidal Love numbers

    International Nuclear Information System (INIS)

    Binnington, Taylor; Poisson, Eric

    2009-01-01

    In Newtonian gravitational theory, a tidal Love number relates the mass multipole moment created by tidal forces on a spherical body to the applied tidal field. The Love number is dimensionless, and it encodes information about the body's internal structure. We present a relativistic theory of Love numbers, which applies to compact bodies with strong internal gravities; the theory extends and completes a recent work by Flanagan and Hinderer, which revealed that the tidal Love number of a neutron star can be measured by Earth-based gravitational-wave detectors. We consider a spherical body deformed by an external tidal field, and provide precise and meaningful definitions for electric-type and magnetic-type Love numbers; and these are computed for polytropic equations of state. The theory applies to black holes as well, and we find that the relativistic Love numbers of a nonrotating black hole are all zero.

  16. Invitation to number theory second edition

    CERN Document Server

    Ore, Oystein

    2017-01-01

    Number theory is the branch of mathematics concerned with the counting numbers, 1, 2, 3, … and their multiples and factors. Of particular importance are odd and even numbers, squares and cubes, and prime numbers. But in spite of their simplicity, you will meet a multitude of topics in this book: magic squares, cryptarithms, finding the day of the week for a given date, constructing regular polygons, pythagorean triples, and many more. In this revised edition, John Watkins and Robin Wilson have updated the text to bring it in line with contemporary developments. They have added new material on Fermat's Last Theorem, the role of computers in number theory, and the use of number theory in cryptography, and have made numerous minor changes in the presentation and layout of the text and the exercises.

  17. Self-correcting random number generator

    Science.gov (United States)

    Humble, Travis S.; Pooser, Raphael C.

    2016-09-06

    A system and method for generating random numbers. The system may include a random number generator (RNG), such as a quantum random number generator (QRNG) configured to self-correct or adapt in order to substantially achieve randomness from the output of the RNG. By adapting, the RNG may generate a random number that may be considered random regardless of whether the random number itself is tested as such. As an example, the RNG may include components to monitor one or more characteristics of the RNG during operation, and may use the monitored characteristics as a basis for adapting, or self-correcting, to provide a random number according to one or more performance criteria.

  18. Observing Optional Number in DDC Edition 23

    Directory of Open Access Journals (Sweden)

    Mohamad Rotmianto

    2015-04-01

    Full Text Available Dewey Decimal Classification is a most popular classification system in the world because of its completeness and most up-to-date. There are many optional number in this classification system, although it rarely to be discussed even it is important to known well about that optional number, especially  for  a  librarian  as  classifier.  This  paper  is  a  literature  study  about  Dewey  Decimal Classification  Edition  23,  to  describe  about  optional  numbers,  particularly  the  number  in relationship with Indonesia’s subject and discipline. This paper is to avoid misunderstanding in interpreted about optional number among librarians, especially for who that does not understand well about optional numbers.

  19. THE DISCOUNTED REPRODUCTIVE NUMBER FOR EPIDEMIOLOGY

    OpenAIRE

    Reluga, Timothy C.; Medlock, Jan; Galvani, Alison

    2009-01-01

    The basic reproductive number, , and the effective reproductive number, , are commonly used in mathematical epidemiology as summary statistics for the size and controllability of epidemics. However, these commonly used reproductive numbers can be misleading when applied to predict pathogen evolution because they do not incorporate the impact of the timing of events in the life-history cycle of the pathogen. To study evolution problems where the host population size is changing, measur...

  20. Defense Horizons. Number 79, April 2015

    Science.gov (United States)

    2015-04-01

    control number. 1. REPORT DATE APR 2015 2. REPORT TYPE 3. DATES COVERED 00-00-2015 to 00-00-2015 4. TITLE AND SUBTITLE Defense Horizons. Number...on the block number of the aircraft. While the maritime inverse synthetic aper - ture radar is available on the new RQ-4 Block 40, a more accessible...maintains a loiter time of approximately 24 hours. Its specifications match exactly what would be called for in this type of mission. However, unlike the

  1. Conferences on Combinatorial and Additive Number Theory

    CERN Document Server

    2014-01-01

    This proceedings volume is based on papers presented at the Workshops on Combinatorial and Additive Number Theory (CANT), which were held at the Graduate Center of the City University of New York in 2011 and 2012. The goal of the workshops is to survey recent progress in combinatorial number theory and related parts of mathematics. The workshop attracts researchers and students who discuss the state-of-the-art, open problems, and future challenges in number theory.

  2. Alternating sums of reciprocal generalized Fibonacci numbers.

    Science.gov (United States)

    Kuhapatanakul, Kantaphon

    2014-01-01

    Recently Holliday and Komatsu extended the results of Ohtsuka and Nakamura on reciprocal sums of Fibonacci numbers to reciprocal sums of generalized Fibonacci numbers. The aim of this work is to give similar results for the alternating sums of reciprocals of the generalized Fibonacci numbers with indices in arithmetic progression. Finally we note our generalizations of some results of Holliday and Komatsu. Primary 11B37; secondary 11B39.

  3. Smoothed analysis of complex conic condition numbers

    OpenAIRE

    Buergisser, Peter; Cucker, Felipe; Lotz, Martin

    2006-01-01

    Smoothed analysis of complexity bounds and condition numbers has been done, so far, on a case by case basis. In this paper we consider a reasonably large class of condition numbers for problems over the complex numbers and we obtain smoothed analysis estimates for elements in this class depending only on geometric invariants of the corresponding sets of ill-posed inputs. These estimates are for a version of smoothed analysis proposed in this paper which, to the best of our knowledge, appears ...

  4. High Atom Number in Microsized Atom Traps

    Science.gov (United States)

    2015-12-14

    Final Performance Report on ONR Grant N00014-12-1-0608 High atom number in microsized atom traps for the period 15 May 2012 through 14 September...TYPE Final Technical Report 3. DATES COVERED (From - To) 05/15/2012-09/14/2012 4. TITLE AND SUBTITLE High atom number in microsized atom traps...forces for implementing a small-footprint, large-number atom -chip instrument. Bichromatic forces rely on absorption and stimulated emission to produce

  5. Maximum Sunspot Numbers and Active Days

    OpenAIRE

    Heon-Young Chang

    2013-01-01

    Parameters associated with solar minimum have been studied to relate them to solar activity at solar maximum so that one could possibly predict behaviors of an upcoming solar cycle. The number of active days has been known as a reliable indicator of solar activity around solar minimum. Active days are days with sunspots reported on the solar disk. In this work, we have explored the relationship between the sunspot numbers at solar maximum and the characteristics of the monthly number...

  6. Analysis of android random number generator

    OpenAIRE

    Sarıtaş, Serkan

    2013-01-01

    Ankara : The Department of Computer Engineering and the Graduate School of Engineering and Science of Bilkent University, 2013. Thesis (Master's) -- Bilkent University, 2013. Includes bibliographical references leaves 61-65. Randomness is a crucial resource for cryptography, and random number generators are critical building blocks of almost all cryptographic systems. Therefore, random number generation is one of the key parts of secure communication. Random number generatio...

  7. Quality pseudo-random number generator

    International Nuclear Information System (INIS)

    Tarasiuk, J.

    1996-01-01

    The pseudo-random number generator (RNG) was written to match needs of nuclear and high-energy physics computation which in some cases require very long and independent random number sequences. In this random number generator the repetition period is about 10 36 what should be sufficient for all computers in the world. In this article the test results of RNG correlation, speed and identity of computations for PC, Sun4 and VAX computer tests are presented

  8. Translations on Western Europe. Number 1321. Communism and Socialism in Italy: Enrico Berlinguer, Bettino Craxi Vie for Power

    Science.gov (United States)

    1978-11-01

    exalting confirmations of his own political genius ." But Romita does not let go and in a new, very lengthy and syntactically complicated statement...P«;T and PCI coes on, with its highs and So the argument between PSI and PCI goes , ± its lows and, as it £**£ lociS Democrat Party [PSDl], Di

  9. The Learning Potentials of Number Blocks

    DEFF Research Database (Denmark)

    Majgaard, Gunver; Nielsen, Jacob; Misfeldt, Morten

    2012-01-01

    . The tool is called Number Blocks and it combines physical interaction, learning, and immediate feedback. Number Blocks supports the children's understanding of place value in the sense that it allows them to experiment with creating large numbers. We found the blocks contributed to the learning process...... in several ways. The blocks combined mathematics and play, and they included and supported children at different academic levels. The auditory representation, especially the enhanced rhythmic effects due to using speech synthesis, and the rhythm helped the children to pronounce large numbers. This creates...

  10. Unique Physician Identification Number (UPIN) Directory

    Data.gov (United States)

    U.S. Department of Health & Human Services — The Unique Physician Identification Number (UPIN) Directory contains selected information on physicians, doctors of Osteopathy, limited licensed practitioners and...

  11. Numbers and prior knowledge in sentence comprehension

    Directory of Open Access Journals (Sweden)

    Pedro Macizo

    2013-01-01

    Full Text Available We evaluated whether the comprehension of sentences that contained numerical information could benefit from presenting numbers in Arabic format and from using prior knowledge. Participants read sentences including numbers (Arabic digits or number words while the comprehension accuracy was evaluated. In addition, the sentences were biased or unbiased by people's prior knowledge about quantities. The results showed better comprehension for sentences that contained Arabic digits as compared to number words. Moreover, biased sentences were understood more accurately than unbiased sentences. These results indicate that information about magnitude in sentence context is comprehended better when quantities are presented in Arabic format and when they are associated with participants' world knowledge.

  12. Numbers and other math ideas come alive

    CERN Document Server

    Pappas, Theoni

    2012-01-01

    Most people don't think about numbers, or take them for granted. For the average person numbers are looked upon as cold, clinical, inanimate objects. Math ideas are viewed as something to get a job done or a problem solved. Get ready for a big surprise with Numbers and Other Math Ideas Come Alive. Pappas explores mathematical ideas by looking behind the scenes of what numbers, points, lines, and other concepts are saying and thinking. In each story, properties and characteristics of math ideas are entertainingly uncovered and explained through the dialogues and actions of its math

  13. Coset Group Construction of Multidimensional Number Systems

    Directory of Open Access Journals (Sweden)

    Horia I. Petrache

    2014-07-01

    Full Text Available Extensions of real numbers in more than two dimensions, in particular quaternions and octonions, are finding applications in physics due to the fact that they naturally capture symmetries of physical systems. However, in the conventional mathematical construction of complex and multicomplex numbers multiplication rules are postulated instead of being derived from a general principle. A more transparent and systematic approach is proposed here based on the concept of coset product from group theory. It is shown that extensions of real numbers in two or more dimensions follow naturally from the closure property of finite coset groups adding insight into the utility of multidimensional number systems in describing symmetries in nature.

  14. Continental anthropogenic primary particle number emissions

    Science.gov (United States)

    Paasonen, Pauli; Kupiainen, Kaarle; Klimont, Zbigniew; Visschedijk, Antoon; Denier van der Gon, Hugo A. C.; Amann, Markus

    2016-06-01

    Atmospheric aerosol particle number concentrations impact our climate and health in ways different from those of aerosol mass concentrations. However, the global, current and future anthropogenic particle number emissions and their size distributions are so far poorly known. In this article, we present the implementation of particle number emission factors and the related size distributions in the GAINS (Greenhouse Gas-Air Pollution Interactions and Synergies) model. This implementation allows for global estimates of particle number emissions under different future scenarios, consistent with emissions of other pollutants and greenhouse gases. In addition to determining the general particulate number emissions, we also describe a method to estimate the number size distributions of the emitted black carbon particles. The first results show that the sources dominating the particle number emissions are different to those dominating the mass emissions. The major global number source is road traffic, followed by residential combustion of biofuels and coal (especially in China, India and Africa), coke production (Russia and China), and industrial combustion and processes. The size distributions of emitted particles differ across the world, depending on the main sources: in regions dominated by traffic and industry, the number size distribution of emissions peaks in diameters range from 20 to 50 nm, whereas in regions with intensive biofuel combustion and/or agricultural waste burning, the emissions of particles with diameters around 100 nm are dominant. In the baseline (current legislation) scenario, the particle number emissions in Europe, Northern and Southern Americas, Australia, and China decrease until 2030, whereas especially for India, a strong increase is estimated. The results of this study provide input for modelling of the future changes in aerosol-cloud interactions as well as particle number related adverse health effects, e.g. in response to tightening

  15. Continental anthropogenic primary particle number emissions

    Directory of Open Access Journals (Sweden)

    P. Paasonen

    2016-06-01

    Full Text Available Atmospheric aerosol particle number concentrations impact our climate and health in ways different from those of aerosol mass concentrations. However, the global, current and future anthropogenic particle number emissions and their size distributions are so far poorly known. In this article, we present the implementation of particle number emission factors and the related size distributions in the GAINS (Greenhouse Gas–Air Pollution Interactions and Synergies model. This implementation allows for global estimates of particle number emissions under different future scenarios, consistent with emissions of other pollutants and greenhouse gases. In addition to determining the general particulate number emissions, we also describe a method to estimate the number size distributions of the emitted black carbon particles. The first results show that the sources dominating the particle number emissions are different to those dominating the mass emissions. The major global number source is road traffic, followed by residential combustion of biofuels and coal (especially in China, India and Africa, coke production (Russia and China, and industrial combustion and processes. The size distributions of emitted particles differ across the world, depending on the main sources: in regions dominated by traffic and industry, the number size distribution of emissions peaks in diameters range from 20 to 50 nm, whereas in regions with intensive biofuel combustion and/or agricultural waste burning, the emissions of particles with diameters around 100 nm are dominant. In the baseline (current legislation scenario, the particle number emissions in Europe, Northern and Southern Americas, Australia, and China decrease until 2030, whereas especially for India, a strong increase is estimated. The results of this study provide input for modelling of the future changes in aerosol–cloud interactions as well as particle number related adverse health effects, e.g. in response

  16. Analytic number theory an introductory course

    CERN Document Server

    Bateman, Paul T

    2004-01-01

    This valuable book focuses on a collection of powerful methods ofanalysis that yield deep number-theoretical estimates. Particularattention is given to counting functions of prime numbers andmultiplicative arithmetic functions. Both real variable ("elementary")and complex variable ("analytic") methods are employed.

  17. Lepton number violation searches at the LHC

    CERN Document Server

    Salvucci, Antonio; The ATLAS collaboration

    2017-01-01

    Lepton number is conserved in the Standard Model, therefore, any evidence for its violation would indicate the existence of new physics. This talk presents a review of the latest searches performed at the LHC concerning Lepton Number Violation (LNV) processes in the context of Left-Right Symmetric theory and Seesaw mechanism.

  18. Hello, I am not an NHS number.

    Science.gov (United States)

    Bates, Jane

    2016-09-14

    I was handed a request to return a patient's call and given a name, signs and symptoms and a number with ten digits, starting with a seven. There was no preceding zero, and assuming it must be a mistake I stuck one on, and dialled. The number was unobtainable.

  19. 20 CFR 404.1220 - Identification numbers.

    Science.gov (United States)

    2010-04-01

    ... 20 Employees' Benefits 2 2010-04-01 2010-04-01 false Identification numbers. 404.1220 Section 404.1220 Employees' Benefits SOCIAL SECURITY ADMINISTRATION FEDERAL OLD-AGE, SURVIVORS AND DISABILITY... will assign a special identification number to each political subdivision included in that modification...

  20. On the Infinitude of the Prime Numbers

    Indian Academy of Sciences (India)

    wherea,b,c,d, .. . , are the successive terms of any increasing arithmetic progression of positive real numbers. Elementary Results. The next result that we shall need is the so-called fundamental theorem of arithmetic: every positive integer greater than 1 can be expressed in precisely one way as a product of prime numbers.

  1. Inhibition, Conflict Detection, and Number Conservation

    Science.gov (United States)

    Lubin, Amélie; Simon, Grégory; Houdé, Olivier; De Neys, Wim

    2015-01-01

    The acquisition of number conservation is a critical step in children's numerical and mathematical development. Classic developmental studies have established that children's number conservation is often biased by misleading intuitions. However, the precise nature of these conservation errors is not clear. A key question is whether conservation…

  2. When Symbolic Spatial Cues Go before Numbers

    Science.gov (United States)

    Herrera, Amparo; Macizo, Pedro

    2011-01-01

    This work explores the effect of spatial cueing on number processing. Participants performed a parity judgment task. However, shortly before the target number, a cue (arrow pointing to left, arrow pointing to right or a cross) was centrally presented. In Experiment 1, in which responses were lateralized, the cue direction modulated the interaction…

  3. On the Concept Image of Complex Numbers

    Science.gov (United States)

    Nordlander, Maria Cortas; Nordlander, Edvard

    2012-01-01

    A study of how Swedish students understand the concept of complex numbers was performed. A questionnaire was issued reflecting the student view of own perception. Obtained answers show a variety of concept images describing how students adopt the concept of complex numbers. These concept images are classified into four categories in order to…

  4. MORPHOLOGY AND CHROMOSOME NUMBERS OF Gongronema ...

    African Journals Online (AJOL)

    journal

    Morphology and chromosome numbers than one nucleus per cell (Partanen, 1963). Polyploidy in some instances is advantageous as it affects plant part sizes like larger leaf areas, flowers and fruits (Walker et al. 2005; El-. Ferchichi et al. 2006; Samiha et al. 2009). The higher number of viable seeds per follicle and matured ...

  5. Neural correlates of merging number words.

    Science.gov (United States)

    Hung, Yi-Hui; Pallier, Christophe; Dehaene, Stanislas; Lin, Yi-Chen; Chang, Acer; Tzeng, Ovid J-L; Wu, Denise H

    2015-11-15

    Complex number words (e.g., "twenty two") are formed by merging together several simple number words (e.g., "twenty" and "two"). In the present study, we explored the neural correlates of this operation and investigated to what extent it engages brain areas involved processing numerical quantity and linguistic syntactic structure. Participants speaking two typologically distinct languages, French and Chinese, were required to read aloud sequences of simple number words while their cerebral activity was recorded by functional magnetic resonance imaging. Each number word could either be merged with the previous ones (e.g., 'twenty three') or not (e.g., 'three twenty'), thus forming four levels ranging from lists of number words to complex numerals. When a number word could be merged with the preceding ones, it was named faster than when it could not. Neuroimaging results showed that the number of merges correlated with activation in the left inferior frontal gyrus and in the left inferior parietal lobule. Consistent findings across Chinese and French participants suggest that these regions serve as the neural bases for forming complex number words in different languages. Copyright © 2015 Elsevier Inc. All rights reserved.

  6. Deafness for the Meanings of Number Words

    Science.gov (United States)

    Cano, Agnes; Rapp, Brenda; Costa, Albert; Juncadella, Montserrat

    2008-01-01

    We describe the performance of an aphasic individual who showed a selective impairment affecting his comprehension of auditorily presented number words and not other word categories. His difficulty in number word comprehension was restricted to the auditory modality, given that with visual stimuli (written words, Arabic numerals and pictures) his…

  7. Search for lepton-family-number nonconservation

    International Nuclear Information System (INIS)

    Hoffman, C.M.

    1986-01-01

    A review of the status of lepton-family-number nonconservation is given. After a brief historical and theoretical discussion, a description of how experimental searches for lepton-family-number nonconservation are performed is presented. Finally, a summary of the results from past experiments and prospects for future experiments is given

  8. Fostering At-Risk Preschoolers' Number Sense

    Science.gov (United States)

    Baroody, Arthur; Eiland, Michael; Thompson, Bradley

    2009-01-01

    Research Findings: A 9-month study served to evaluate the effectiveness of a pre-kindergarten number sense curriculum. Phase 1 of the intervention involved manipulative-, game-based number sense instruction; Phase 2, computer-aided mental-arithmetic training with the simplest sums. Eighty 4- and 5-year-olds at risk for school failure were randomly…

  9. Atomic Fisher information versus atomic number

    International Nuclear Information System (INIS)

    Nagy, A.; Sen, K.D.

    2006-01-01

    It is shown that the Thomas-Fermi Fisher information is negative. A slightly more sophisticated model proposed by Gaspar provides a qualitatively correct expression for the Fisher information: Gaspar's Fisher information is proportional to the two-third power of the atomic number. Accurate numerical calculations show an almost linear dependence on the atomic number

  10. Cellular Automata Rules and Linear Numbers

    OpenAIRE

    Nayak, Birendra Kumar; Sahoo, Sudhakar; Biswal, Sagarika

    2012-01-01

    In this paper, linear Cellular Automta (CA) rules are recursively generated using a binary tree rooted at "0". Some mathematical results on linear as well as non-linear CA rules are derived. Integers associated with linear CA rules are defined as linear numbers and the properties of these linear numbers are studied.

  11. Estimating Avogadro's number from skylight and airlight

    Science.gov (United States)

    Pesic, Peter

    2005-01-01

    Naked-eye determinations of the visual range yield order-of-magnitude estimates of Avogadro's number, using an argument of Rayleigh. Alternatively, by looking through a cardboard tube, we can compare airlight and skylight and give another estimate of this number using the law of atmospheres.

  12. Hacking DNA copy number for circuit engineering.

    Science.gov (United States)

    Wu, Feilun; You, Lingchong

    2017-07-27

    DNA copy number represents an essential parameter in the dynamics of synthetic gene circuits but typically is not explicitly considered. A new study demonstrates how dynamic control of DNA copy number can serve as an effective strategy to program robust oscillations in gene expression circuits.

  13. IEEE Standard for Floating Point Numbers

    Indian Academy of Sciences (India)

    IAS Admin

    This is a conservative definition used by industry. In MATLAB, machine epsilon is as defined above. However, academics define machine epsilon as the upper bound of the relative error when numbers are rounded. Thus, for 32-bit floating point numbers, the machine epsilon is 2–23/2. 5.96 ×10–8. The machine epsilon is ...

  14. Factors Influencing Number of Physiotherapy Treatment Sessions ...

    African Journals Online (AJOL)

    Little is known about the influence of physiotherapists' characteristics and treatment modalities on the number of treatment sessions in Nigeria. This study was designed to evaluate the factors influencing the number of treatment sessions for patients with low back pain (LBP). Three hundred and eleven practising ...

  15. 41 CFR 105-1.109 - Numbering.

    Science.gov (United States)

    2010-07-01

    ... 41 Public Contracts and Property Management 3 2010-07-01 2010-07-01 false Numbering. 105-1.109 Section 105-1.109 Public Contracts and Property Management Federal Property Management Regulations System (Continued) GENERAL SERVICES ADMINISTRATION 1-INTRODUCTION 1.1-Regulations System § 105-1.109 Numbering. ...

  16. 7 CFR 46.20 - Lot numbers.

    Science.gov (United States)

    2010-01-01

    ... and entered on all sales tickets identifying and segregating the sales from the various shipments on hand. The lot number shall be entered on the sales tickets by the salesmen at the time of sale or by the produce dispatcher, and not by bookkeepers or others after the sales have been made. No lot number...

  17. On contact numbers in random rod packings

    NARCIS (Netherlands)

    Wouterse, A.; Luding, Stefan; Philipse, A.P.

    2009-01-01

    Random packings of non-spherical granular particles are simulated by combining mechanical contraction and molecular dynamics, to determine contact numbers as a function of density. Particle shapes are varied from spheres to thin rods. The observed contact numbers (and packing densities) agree well

  18. Comments on nonparametric predictions of sunspot numbers

    DEFF Research Database (Denmark)

    Jensen, J.L.

    1993-01-01

    Recent results of Cerrito (1990) are criticized, and the level of unexplainable noise in the observed series of sunspot numbers is discussed.......Recent results of Cerrito (1990) are criticized, and the level of unexplainable noise in the observed series of sunspot numbers is discussed....

  19. The Ramsey Numbers of Paths Versus Fans

    NARCIS (Netherlands)

    Salman, M.; Broersma, Haitze J.; Faigle, U.; Hurink, Johann L.; Pickl, Stefan; Woeginger, Gerhard

    2003-01-01

    For two given graphs G and H, the Ramsey number R(G,H) is the smallest positive integer p such that for every graph F on p vertices the following holds: either F contains G as a subgraph or the complement of F contains H as a subgraph. In this paper, we study the Ramsey numbers R(Pn,Fm), where Pn is

  20. Ramsey numbers and adiabatic quantum computing.

    Science.gov (United States)

    Gaitan, Frank; Clark, Lane

    2012-01-06

    The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers R(m,n) with m, n≥3, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers R(m,n). We show how the computation of R(m,n) can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for 5≤s≤7. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class quantum Merlin Arthur.

  1. A conversational introduction to algebraic number theory

    CERN Document Server

    Pollack, Paul

    2017-01-01

    Gauss famously referred to mathematics as the "queen of the sciences" and to number theory as the "queen of mathematics". This book is an introduction to algebraic number theory, meaning the study of arithmetic in finite extensions of the rational number field \\mathbb{Q}. Originating in the work of Gauss, the foundations of modern algebraic number theory are due to Dirichlet, Dedekind, Kronecker, Kummer, and others. This book lays out basic results, including the three "fundamental theorems": unique factorization of ideals, finiteness of the class number, and Dirichlet's unit theorem. While these theorems are by now quite classical, both the text and the exercises allude frequently to more recent developments. In addition to traversing the main highways, the book reveals some remarkable vistas by exploring scenic side roads. Several topics appear that are not present in the usual introductory texts. One example is the inclusion of an extensive discussion of the theory of elasticity, which provides a precise w...

  2. Topics from the theory of numbers

    CERN Document Server

    Grosswald, Emil

    1984-01-01

    Many of the important and creative developments in modern mathematics resulted from attempts to solve questions that originate in number theory. The publication of Emil Grosswald’s classic text presents an illuminating introduction to number theory. Combining the historical developments with the analytical approach, Topics from the Theory of Numbers offers the reader a diverse range of subjects to investigate, including: * divisibility * congruences * the Riemann zeta function * Diophantine equations and Fermat’s conjecture * the theory of partitions Comprehensive in nature, Topics from the Theory of Numbers is an ideal text for advanced undergraduates and graduate students alike. "In my opinion it is excellent. It is carefully written and represents clearly a work of a scholar who loves and understands his subject. One can only wish more authors would take such pains and would be as good and honest expositors as Grosswald." — Marc Kac "This book is designed for use in a first course in number theory at...

  3. Complex numbers from A to Z

    CERN Document Server

    Andreescu, Titu

    2014-01-01

    It is impossible to imagine modern mathematics without complex numbers. The second edition of Complex Numbers from A to … Z introduces the reader to this fascinating subject that, from the time of L. Euler, has become one of the most utilized ideas in mathematics. The exposition concentrates on key concepts and then elementary results concerning these numbers. The reader learns how complex numbers can be used to solve algebraic equations and to understand the geometric interpretation of complex numbers and the operations involving them. The theoretical parts of the book are augmented with rich exercises and problems at various levels of difficulty. Many new problems and solutions have been added in this second edition. A special feature of the book is the last chapter, a selection of outstanding Olympiad and other important mathematical contest problems solved by employing the methods already presented. The book reflects the unique experience of the authors. It distills a vast mathematical literature, most ...

  4. Random numbers spring from alpha decay

    International Nuclear Information System (INIS)

    Frigerio, N.A.; Sanathanan, L.P.; Morley, M.; Clark, N.A.; Tyler, S.A.

    1980-05-01

    Congruential random number generators, which are widely used in Monte Carlo simulations, are deficient in that the number they generate are concentrated in a relatively small number of hyperplanes. While this deficiency may not be a limitation in small Monte Carlo studies involving a few variables, it introduces a significant bias in large simulations requiring high resolution. This bias was recognized and assessed during preparations for an accident analysis study of nuclear power plants. This report describes a random number device based on the radioactive decay of alpha particles from a 235 U source in a high-resolution gas proportional counter. The signals were fed to a 4096-channel analyzer and for each channel the frequency of signals registered in a 20,000-microsecond interval was recorded. The parity bits of these frequency counts (0 for an even count and 1 for an odd count) were then assembled in sequence to form 31-bit binary random numbers and transcribed to a magnetic tape. This cycle was repeated as many times as were necessary to create 3 million random numbers. The frequency distribution of counts from the present device conforms to the Brockwell-Moyal distribution, which takes into account the dead time of the counter (both the dead time and decay constant of the underlying Poisson process were estimated). Analysis of the count data and tests of randomness on a sample set of the 31-bit binary numbers indicate that this random number device is a highly reliable source of truly random numbers. Its use is, therefore, recommended in Monte Carlo simulations for which the congruential pseudorandom number generators are found to be inadequate. 6 figures, 5 tables

  5. Number Worlds: Visual and Experimental Access to Elementary Number Theory Concepts

    Science.gov (United States)

    Sinclair, Nathalie; Zazkis, Rina; Liljedahl, Peter

    2004-01-01

    Recent research demonstrates that many issues related to the structure of natural numbers and the relationship among numbers are not well grasped by students. In this article, we describe a computer-based learning environment called "Number Worlds" that was designed to support the exploration of elementary number theory concepts by…

  6. Alternative analysis: the prime numbers theory and an extension of the real numbers set

    OpenAIRE

    Sukhotin A.; Zvyagin M.

    2016-01-01

    Here we consider the theory of prime numbers at a new methodology. The theory of prime numbers is one of the most ancient mathematical branches. We found an estimate of the all prime numbers sum using the notions of infinite lager numbers and infinitely small numbers, farther we estimated the value of the maximal prime number. We proved that Hardy–Littlewood Hypothesis has the positive decision too. The infinite small numbers define a new methodology of the well–known function o(x) applicatio...

  7. Bernoulli-Carlitz and Cauchy-Carlitz numbers with Stirling-Carlitz numbers

    OpenAIRE

    Kaneko, Hajime; Komatsu, Takao

    2017-01-01

    Recently, the Cauchy-Carlitz number was defined as the counterpart of the Bernoulli-Carlitz number. Both numbers can be expressed explicitly in terms of so-called Stirling-Carlitz numbers. In this paper, we study the second analogue of Stirling-Carlitz numbers and give some general formulae, including Bernoulli and Cauchy numbers in formal power series with complex coefficients, and Bernoulli-Carlitz and Cauchy-Carlitz numbers in function fields. We also give some applications of Hasse-Teichm...

  8. Low Nephron Number and Its Clinical Consequences

    Directory of Open Access Journals (Sweden)

    Valerie A. Luyckx

    2011-10-01

    Full Text Available decades ago, that developmental programming of the kidney impacts an individual’s risk for hypertension and renal disease in later life. Low birth weight is the strongest current clinical surrogate marker for an adverse intrauterine environment and, based on animal and human studies, is associated with a low nephron number. Other clinical correlates of low nephron number include female gender, short adult stature, small kidney size, and prematurity. Low nephron number in Caucasian and Australian Aboriginal subjects has been shown to be associated with higher blood pressures, and, conversely, hypertension is less prevalent in individuals with higher nephron numbers. In addition to nephron number, other programmed factors associated with the increased risk of hypertension include salt sensitivity, altered expression of renal sodium transporters, altered vascular reactivity, and sympathetic nervous system overactivity. Glomerular volume is universally found to vary inversely with nephron number, suggesting a degree of compensatory hypertrophy and hyperfunction in the setting of a low nephron number. This adaptation may become overwhelmed in the setting of superimposed renal insults, e.g. diabetes mellitus or rapid catch-up growth, leading to the vicious cycle of on-going hyperfiltration, proteinuria, nephron loss and progressive renal functional decline. Many millions of babies are born with low birth weight every year, and hypertension and renal disease prevalences are increasing around the globe. At present, little can be done clinically to augment nephron number; therefore adequate prenatal care and careful postnatal nutrition are crucial to optimize an individual’s nephron number during development and potentially to stem the tide of the growing cardiovascular and renal disease epidemics worldwide.

  9. Numbers at work a cultural perspective

    CERN Document Server

    Taschner , Rudolf

    2007-01-01

    Drawing primarily from historical examples, this book explains the tremendous role that numbers and, in particular, mathematics play in all aspects of our civilization and culture. The lively style and illustrative examples will engage the reader who wants to understand the many ways in which mathematics enables science, technology, art, music, politics, and rational foundations of human thought. Each chapter focuses on the influence of mathematics in a specific field and on a specific historical figure, such as ""Pythagoras: Numbers and Symbol""; ""Bach: Numbers and Music""; ""Descartes: Numb

  10. Algebraic Geometry and Number Theory Summer School

    CERN Document Server

    Sarıoğlu, Celal; Soulé, Christophe; Zeytin, Ayberk

    2017-01-01

    This lecture notes volume presents significant contributions from the “Algebraic Geometry and Number Theory” Summer School, held at Galatasaray University, Istanbul, June 2-13, 2014. It addresses subjects ranging from Arakelov geometry and Iwasawa theory to classical projective geometry, birational geometry and equivariant cohomology. Its main aim is to introduce these contemporary research topics to graduate students who plan to specialize in the area of algebraic geometry and/or number theory. All contributions combine main concepts and techniques with motivating examples and illustrative problems for the covered subjects. Naturally, the book will also be of interest to researchers working in algebraic geometry, number theory and related fields.

  11. Topological quantum numbers in nonrelativistic physics

    CERN Document Server

    Thouless, David James

    1998-01-01

    Topological quantum numbers are distinguished from quantum numbers based on symmetry because they are insensitive to the imperfections of the systems in which they are observed. They have become very important in precision measurements in recent years, and provide the best measurements of voltage and electrical resistance. This book describes the theory of such quantum numbers, starting with Dirac's argument for the quantization of electric charge, and continuing with discussions on the helium superfluids, flux quantization and the Josephson effect in superconductors, the quantum Hall effect,

  12. Standard random number generation for MBASIC

    Science.gov (United States)

    Tausworthe, R. C.

    1976-01-01

    A machine-independent algorithm is presented and analyzed for generating pseudorandom numbers suitable for the standard MBASIC system. The algorithm used is the polynomial congruential or linear recurrence modulo 2 method. Numbers, formed as nonoverlapping adjacent 28-bit words taken from the bit stream produced by the formula a sub m + 532 = a sub m + 37 + a sub m (modulo 2), do not repeat within the projected age of the solar system, show no ensemble correlation, exhibit uniform distribution of adjacent numbers up to 19 dimensions, and do not deviate from random runs-up and runs-down behavior.

  13. Recognition of the smart card iconic numbers

    Directory of Open Access Journals (Sweden)

    Xin Xue Shi

    2016-01-01

    Full Text Available Manual way of recognizing and inputting the smart card iconic numbers leads to much time consuming, high resources consuming and low accuracy. This paper presents a new automatic method based on the technology of computer vision, including Harr operator for face detection, Fast operator for number location, image binarization, character segmentation and BP neural network for number recognition. Experimental results on 100 ID cards show that by adjusting the parameters of the BP neural network properly, the recognition accuracy is more than 99%, and the recognition time for each ID card is within 0.05 seconds.

  14. Complex Binary Number System Algorithms and Circuits

    CERN Document Server

    Jamil, Tariq

    2013-01-01

    This book is a compilation of the entire research work on the topic of Complex Binary Number System (CBNS) carried out by the author as the principal investigator and members of his research groups at various universities during the years 1992-2012. Pursuant to these efforts spanning several years, the realization of CBNS as a viable alternative to represent complex numbers in an 'all-in-one' binary number format has become possible and efforts are underway to build computer hardware based on this unique number system. It is hoped that this work will be of interest to anyone involved in computer arithmetic and digital logic design and kindle renewed enthusiasm among the engineers working in the areas of digital signal and image processing for developing newer and efficient algorithms and techniques incorporating CBNS.

  15. Muon number nonconservation in gauge theories

    International Nuclear Information System (INIS)

    Cheng, T.P.; Li, L.F.

    1977-01-01

    The question of separate conservation of muon and electron number is considered in the context of unified gauge theories of weak and electromagnetic interactions. Theories with heavy neutral leptons, Higgs scalars, and doubly charged heavy leptons are discussed. 28 references

  16. Distribution function of faint galaxy numbers

    International Nuclear Information System (INIS)

    Fesenko, L.M.

    1981-01-01

    The Lick observatory counts of galaxies are considered. The distribution of number of galaxies in elementary regions (ER) of 1 degx1 deg is investigated. Each field of 6 degx6 deg was treated separately At b>40 deg the probab+lity to observe of n galaxies in ER is an exponential decreasing function of n, if unequality n> were fulfilled. The mean apparent multiplicity of a galaxy (2.8+-0.9) was derived. The galaxy number distribution was simple model for the number of various systems of galaxies. The supperclustering of galaxies was not introduced. Based on that model the approximate expression for galaxy number distribution was considered and was compared with observed distributions. The agreement between these distributions become better with reducing of the interstellar absorption of light

  17. Chaotic behaviour of high Mach number flows

    Science.gov (United States)

    Varvoglis, H.; Ghosh, S.

    1985-01-01

    The stability of the super-Alfvenic flow of a two-fluid plasma model with respect to the Mach number and the angle between the flow direction and the magnetic field is investigated. It is found that, in general, a large scale chaotic region develops around the initial equilibrium of the laminar flow when the Mach number exceeds a certain threshold value. After reaching a maximum the size of this region begins shrinking and goes to zero as the Mach number tends to infinity. As a result high Mach number flows in time independent astrophysical plasmas may lead to the formation of 'quasi-shocks' in the presence of little or no dissipation.

  18. The Power of Numbers in Global Governance

    DEFF Research Database (Denmark)

    Krause Hansen, Hans; Mühlen-Schulte, Arthur

    2012-01-01

    at a distance in the global political economy. It argues that the use of numbers in global governance should not be regarded only as a platform for knowledge sharing and learning. More than this, it needs to be understood in broader terms as a mechanism of inclusion and exclusion from complex social hierarchies......The deployment of numbers have become a sine qua non in governance practices worldwide in recent decades. But the reasons behind this development and its implications for governance practices have not been systematically researched and theorised. This introductory article provides a short overview...... of the historical and contemporary role of numbers in different governance settings. It includes a discussion of the capacity of numbers to foster social identities, relations and truths across national boundaries, to construct issue areas and to enable various modes of surveillance, communication and action...

  19. Bone Mass Measurement: What the Numbers Mean

    Science.gov (United States)

    ... the Test Do? The T-Score World Health Organization Definitions Based on Bone Density Levels Low Bone Mass ... number, the more severe the osteoporosis. World Health Organization Definitions Based on Bone Density Levels Level Definition Normal ...

  20. The rise of number agreement in Nheengatu

    Directory of Open Access Journals (Sweden)

    Aline da Cruz

    Full Text Available Abstract: Number agreement systems often present traces of older elements common to different languages of the same family; thus, their emergence is difficult to reconstruct. One possible origin of such systems is the grammaticalization of plural words into bound morphemes, which, as a result of a long process, develop into agreement markers and may become obligatory. Various investigations have provided evidence for this hypothesis. However, the complete process of change from a system with no number as grammatical category into a number agreement system in a single language has not been documented. This paper analyses documents covering different stages of the development of the Nheengatu language from Tupinambá in order to observe how the number agreement system emerged in modern Nheengatu. By doing so, this paper supports the idea that grammaticalization may have occurred rapidly in intense contact situations.

  1. Gateway Newsletter. Volume 14. Number 1, 2003

    National Research Council Canada - National Science Library

    Johnston, Judith

    2003-01-01

    .... The Human Systems Information Analysis Center (HSIAC) is the gateway to worldwide sources of up-to-date human systems information for designers, engineers, researchers, and number factors specialists...

  2. Introduction to the geometry of complex numbers

    CERN Document Server

    Deaux, Roland

    2008-01-01

    Geared toward readers unfamiliar with complex numbers, this text explains how to solve problems that frequently arise in the applied sciences and emphasizes constructions related to algebraic operations. 1956 edition.

  3. Opening the Door on Triangular Numbers

    Science.gov (United States)

    McMartin, Kimberley; McMaster, Heather

    2016-01-01

    As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.

  4. Generation of pseudo-random numbers

    Science.gov (United States)

    Howell, L. W.; Rheinfurth, M. H.

    1982-01-01

    Practical methods for generating acceptable random numbers from a variety of probability distributions which are frequently encountered in engineering applications are described. The speed, accuracy, and guarantee of statistical randomness of the various methods are discussed.

  5. A brief introduction to particle number estimation

    DEFF Research Database (Denmark)

    Dorph-Petersen, Karl-Anton; Nyengaard, Jens Randel; Gundersen, Hans Jørgen Gottlieb

    1998-01-01

    The principle of particle number estimation using the disector is described emphasising the practical similarities and differences in the application of the principle in biomedicine and non-biological sciences....

  6. Microcomputer-Assisted Discoveries: Random Numbers.

    Science.gov (United States)

    Kimberling, Clark

    1983-01-01

    A programing contest was designed to promote interest in mathematical randomness. Student-developed programs making clever uses of random numbers are presented. Modifications users might make are suggested. (MNS)

  7. Using Random Numbers in Science Research Activities.

    Science.gov (United States)

    Schlenker, Richard M.; And Others

    1996-01-01

    Discusses the importance of science process skills and describes ways to select sets of random numbers for selection of subjects for a research study in an unbiased manner. Presents an activity appropriate for grades 5-12. (JRH)

  8. Clinching First Place: Calculating the Magic Number.

    Science.gov (United States)

    Quinn, Robert J.

    2000-01-01

    Describes a lesson plan in which students apply their mathematical intuition to determine win-loss possibilities of teams in a sports league and develop a formula for calculating the magic number for clinching first place. (YDS)

  9. Hodge numbers for all CICY quotients

    Energy Technology Data Exchange (ETDEWEB)

    Constantin, Andrei [Department of Physics and Astronomy, Uppsala University, SE-751 20, Uppsala (Sweden); Gray, James [Physics Department, Robeson Hall, Virginia Tech,Blacksburg, VA 24061 (United States); Lukas, Andre [Rudolf Peierls Centre for Theoretical Physics, Oxford University,1 Keble Road, Oxford, OX1 3NP (United Kingdom)

    2017-01-02

    We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification http://dx.doi.org/10.1007/JHEP04(2011)005.

  10. Fibonacci and Lucas numbers with applications

    CERN Document Server

    Koshy, Thomas

    2011-01-01

    [Koshy's] book is without doubt the most comprehensive and scholarly work on Fibonacci numbers to date and I am sure that it will quickly signal its presence and impose itself as an authoritative reference manual on Fibonacci numbers. -Napoleon Gauthier, Royal Military College of Canada, Kingston, ON What a gem this is! [...] My only regrest about the book is that it wasn't around years ago. It fills such a void. -Monte Zerger, Adams State College, Alamosa, CO

  11. Random Number Generation for High Performance Computing

    Science.gov (United States)

    2015-01-01

    Memory (DRAM), Double Data Rate Random Access Memory ( DDR RAM ), Static Random Access Memory (SRAM), Extended Data Out Random Access 45 Memory (EDO RAM ...Random Access Memory ( DDR RAM ), Static Random Access Memory (SRAM), Extended Data Out Random Access Memory (EDO RAM ), Rambus Random Access 20 Memory...FTE Equivalent: Total Number: PERCENT_SUPPORTEDNAME FTE Equivalent: Total Number: National Academy Member Rajendra V. Boppana 0.30 Ram C. Tripathi 0.08

  12. Some inequalities for the Bell numbers

    Indian Academy of Sciences (India)

    Feng Qi

    2017-08-19

    Aug 19, 2017 ... 428–431; available online at doi:10.1016/0022-247X(84)90006-4. [16] Qi F, An explicit formula for the Bell numbers in terms of the Lah and Stirling numbers, Mediterr. J. Math. 13(5) (2016) 2795–2800; available online at doi:10.1007/ · s00009-015-0655-7. [17] Qi F, Generalized weighted mean values with ...

  13. Number Albedo of Low-Energy Photons

    International Nuclear Information System (INIS)

    Ljubenov, V.; Simovic, R.; Markovic, S.

    2007-01-01

    Number albedo of water, aluminum and iron for incident photons in energy range from 20 keV to 100 keV is presented in this paper. Results are obtained through the Monte Carlo simulations of photon reflection by using the MCNP, FOTELP and PENELOPE computer codes. Calculated values are compared with the classical data published by B. P. Bulatov and his collaborators. Influence of the fluorescence yield to the photon number albedo of iron target is analyzed in detail. (author)

  14. Bethe's quantum numbers and rigged configurations

    Directory of Open Access Journals (Sweden)

    Anatol N. Kirillov

    2016-04-01

    Full Text Available We propose a method to determine the quantum numbers, which we call the rigged configurations, for the solutions to the Bethe ansatz equations for the spin-1/2 isotropic Heisenberg model under the periodic boundary condition. Our method is based on the observation that the sums of Bethe's quantum numbers within each string behave particularly nicely. We confirm our procedure for all solutions for length 12 chain (totally 923 solutions.

  15. On Fibonacci Numbers Which Are Elliptic Carmichael

    Science.gov (United States)

    2014-12-27

    On Fibonacci numbers which are elliptic Carmichael Florian Luca School of Mathematics University of the Witwatersrand P. O. Box Wits 2050, South...CM elliptic curve with CM field different from Q( √ −1), then the set of n for which the nth Fibonacci number Fn is elliptic Carmichael for E is of...Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law

  16. Hodge numbers for all CICY quotients

    International Nuclear Information System (INIS)

    Constantin, Andrei; Gray, James; Lukas, Andre

    2017-01-01

    We present a general method for computing Hodge numbers for Calabi-Yau manifolds realised as discrete quotients of complete intersections in products of projective spaces. The method relies on the computation of equivariant cohomologies and is illustrated for several explicit examples. In this way, we compute the Hodge numbers for all discrete quotients obtained in Braun’s classification http://dx.doi.org/10.1007/JHEP04(2011)005.

  17. All-optical fast random number generator.

    Science.gov (United States)

    Li, Pu; Wang, Yun-Cai; Zhang, Jian-Zhong

    2010-09-13

    We propose a scheme of all-optical random number generator (RNG), which consists of an ultra-wide bandwidth (UWB) chaotic laser, an all-optical sampler and an all-optical comparator. Free from the electric-device bandwidth, it can generate 10Gbit/s random numbers in our simulation. The high-speed bit sequences can pass standard statistical tests for randomness after all-optical exclusive-or (XOR) operation.

  18. Large number discrimination in newborn fish.

    Directory of Open Access Journals (Sweden)

    Laura Piffer

    Full Text Available Quantitative abilities have been reported in a wide range of species, including fish. Recent studies have shown that adult guppies (Poecilia reticulata can spontaneously select the larger number of conspecifics. In particular the evidence collected in literature suggest the existence of two distinct systems of number representation: a precise system up to 4 units, and an approximate system for larger numbers. Spontaneous numerical abilities, however, seem to be limited to 4 units at birth and it is currently unclear whether or not the large number system is absent during the first days of life. In the present study, we investigated whether newborn guppies can be trained to discriminate between large quantities. Subjects were required to discriminate between groups of dots with a 0.50 ratio (e.g., 7 vs. 14 in order to obtain a food reward. To dissociate the roles of number and continuous quantities that co-vary with numerical information (such as cumulative surface area, space and density, three different experiments were set up: in Exp. 1 number and continuous quantities were simultaneously available. In Exp. 2 we controlled for continuous quantities and only numerical information was available; in Exp. 3 numerical information was made irrelevant and only continuous quantities were available. Subjects successfully solved the tasks in Exp. 1 and 2, providing the first evidence of large number discrimination in newborn fish. No discrimination was found in experiment 3, meaning that number acuity is better than spatial acuity. A comparison with the onset of numerical abilities observed in shoal-choice tests suggests that training procedures can promote the development of numerical abilities in guppies.

  19. Persistent consequences of atypical early number concepts

    Directory of Open Access Journals (Sweden)

    Michèle M. M. Mazzocco

    2013-09-01

    Full Text Available How does symbolic number knowledge performance help identify young children at risk for poor mathematics achievement outcomes? In research and practice, classification of mathematics learning disability (MLD, or dyscalculia is typically based on composite scores from broad measures of mathematics achievement. These scores do predict later math achievement levels, but do not specify the nature of math difficulties likely to emerge among students at greatest risk for long-term mathematics failure. Here we report that gaps in 2nd and 3rd graders’ number knowledge predict specific types of errors made on math assessments at Grade 8. Specifically, we show that early whole number misconceptions predict slower and less accurate performance, and atypical computational errors, on Grade 8 arithmetic tests. We demonstrate that basic number misconceptions can be detected by idiosyncratic responses to number knowledge items, and that when such misconceptions are evident during primary school they persist throughout the school age years, with variable manifestation throughout development. We conclude that including specific qualitative assessments of symbolic number knowledge in primary school may provide greater specificity of the types of difficulties likely to emerge among students at risk for poor mathematics outcomes.

  20. Complex architecture of primes and natural numbers.

    Science.gov (United States)

    García-Pérez, Guillermo; Serrano, M Ángeles; Boguñá, Marián

    2014-08-01

    Natural numbers can be divided in two nonoverlapping infinite sets, primes and composites, with composites factorizing into primes. Despite their apparent simplicity, the elucidation of the architecture of natural numbers with primes as building blocks remains elusive. Here, we propose a new approach to decoding the architecture of natural numbers based on complex networks and stochastic processes theory. We introduce a parameter-free non-Markovian dynamical model that naturally generates random primes and their relation with composite numbers with remarkable accuracy. Our model satisfies the prime number theorem as an emerging property and a refined version of Cramér's conjecture about the statistics of gaps between consecutive primes that seems closer to reality than the original Cramér's version. Regarding composites, the model helps us to derive the prime factors counting function, giving the probability of distinct prime factors for any integer. Probabilistic models like ours can help to get deeper insights about primes and the complex architecture of natural numbers.

  1. Number skills are maintained in healthy ageing.

    Science.gov (United States)

    Cappelletti, Marinella; Didino, Daniele; Stoianov, Ivilin; Zorzi, Marco

    2014-03-01

    Numerical skills have been extensively studied in terms of their development and pathological decline, but whether they change in healthy ageing is not well known. Longer exposure to numbers and quantity-related problems may progressively refine numerical skills, similar to what happens to other cognitive abilities like verbal memory. Alternatively, number skills may be sensitive to ageing, reflecting either a decline of number processing itself or of more auxiliary cognitive abilities that are involved in number tasks. To distinguish between these possibilities we tested 30 older and 30 younger participants on an established numerosity discrimination task requiring to judge which of two sets of items is more numerous, and on arithmetical tasks. Older participants were remarkably accurate in performing arithmetical tasks although their numerosity discrimination (also known as 'number acuity') was impaired. Further analyses indicate that this impairment was limited to numerosity trials requiring inhibiting information incongruent to numerosity (e.g., fewer but larger items), and that this also correlated with poor inhibitory processes measured by standard tests. Therefore, rather than a numerical impairment, poor numerosity discrimination is likely to reflect elderly's impoverished inhibitory processes. This conclusion is supported by simulations with a recent neuro-computational model of numerosity perception, where only the specific degradation of inhibitory processes produced a pattern that closely resembled older participants' performance. Numeracy seems therefore resilient to ageing but it is influenced by the decline of inhibitory processes supporting number performance, consistent with the 'Inhibitory Deficit' Theory. Copyright © 2013 Elsevier Inc. All rights reserved.

  2. The deep history of the number words.

    Science.gov (United States)

    Pagel, Mark; Meade, Andrew

    2017-02-19

    We have previously shown that the 'low limit' number words (from one to five) have exceptionally slow rates of lexical replacement when measured across the Indo-European (IE) languages. Here, we replicate this finding within the Bantu and Austronesian language families, and with new data for the IE languages. Number words can remain stable for 10 000 to over 100 000 years, or around 3.5-20 times longer than average rates of lexical replacement among the Swadesh list of 'fundamental vocabulary' items. Ordinal evidence suggests that number words also have slow rates of lexical replacement in the Pama-Nyungan language family of Australia. We offer three hypotheses to explain these slow rates of replacement: (i) that the abstract linguistic-symbolic processing of 'number' links to evolutionarily conserved brain regions associated with numerosity; (ii) that number words are unambiguous and therefore have lower 'mutation rates'; and (iii) that the number words occupy a region of the phonetic space that is relatively full and therefore resist change because alternatives are unlikely to be as 'good' as the original word.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

  3. A new pseudorandom number generator based on a complex number chaotic equation

    International Nuclear Information System (INIS)

    Liu Yang; Tong Xiao-Jun

    2012-01-01

    In recent years, various chaotic equation based pseudorandom number generators have been proposed. However, the chaotic equations are all defined in the real number field. In this paper, an equation is proposed and proved to be chaotic in the imaginary axis. And a pseudorandom number generator is constructed based on the chaotic equation. The alteration of the definitional domain of the chaotic equation from the real number field to the complex one provides a new approach to the construction of chaotic equations, and a new method to generate pseudorandom number sequences accordingly. Both theoretical analysis and experimental results show that the sequences generated by the proposed pseudorandom number generator possess many good properties

  4. Approximate particle number projection in hot nuclei

    International Nuclear Information System (INIS)

    Kosov, D.S.; Vdovin, A.I.

    1995-01-01

    Heated finite systems like, e.g., hot atomic nuclei have to be described by the canonical partition function. But this is a quite difficult technical problem and, as a rule, the grand canonical partition function is used in the studies. As a result, some shortcomings of the theoretical description appear because of the thermal fluctuations of the number of particles. Moreover, in nuclei with pairing correlations the quantum number fluctuations are introduced by some approximate methods (e.g., by the standard BCS method). The exact particle number projection is very cumbersome and an approximate number projection method for T ≠ 0 basing on the formalism of thermo field dynamics is proposed. The idea of the Lipkin-Nogami method to perform any operator as a series in the number operator powers is used. The system of equations for the coefficients of this expansion is written and the solution of the system in the next approximation after the BCS one is obtained. The method which is of the 'projection after variation' type is applied to a degenerate single j-shell model. 14 refs., 1 tab

  5. True random numbers from amplified quantum vacuum.

    Science.gov (United States)

    Jofre, M; Curty, M; Steinlechner, F; Anzolin, G; Torres, J P; Mitchell, M W; Pruneri, V

    2011-10-10

    Random numbers are essential for applications ranging from secure communications to numerical simulation and quantitative finance. Algorithms can rapidly produce pseudo-random outcomes, series of numbers that mimic most properties of true random numbers while quantum random number generators (QRNGs) exploit intrinsic quantum randomness to produce true random numbers. Single-photon QRNGs are conceptually simple but produce few random bits per detection. In contrast, vacuum fluctuations are a vast resource for QRNGs: they are broad-band and thus can encode many random bits per second. Direct recording of vacuum fluctuations is possible, but requires shot-noise-limited detectors, at the cost of bandwidth. We demonstrate efficient conversion of vacuum fluctuations to true random bits using optical amplification of vacuum and interferometry. Using commercially-available optical components we demonstrate a QRNG at a bit rate of 1.11 Gbps. The proposed scheme has the potential to be extended to 10 Gbps and even up to 100 Gbps by taking advantage of high speed modulation sources and detectors for optical fiber telecommunication devices.

  6. Unpredictability and the transmission of numbers

    Science.gov (United States)

    Myers, John M.; Madjid, F. Hadi

    2016-03-01

    Curiously overlooked in physics is its dependence on the transmission of numbers. For example, the transmission of numerical clock readings is implicit in the concept of a coordinate system. The transmission of numbers and other logical distinctions is often achieved over a computer-mediated communications network in the face of an unpredictable environment. By unpredictable we mean something stronger than the spread of probabilities over given possible outcomes, namely an opening to unforeseeable possibilities. Unpredictability, until now overlooked in theoretical physics, makes the transmission of numbers interesting. Based on recent proofs within quantum theory that provide a theoretical foundation to unpredictability, here we show how regularities in physics rest on a background of channels over which numbers are transmitted. As is known to engineers of digital communications, numerical transmissions depend on coordination reminiscent of the cycle of throwing and catching by players tossing a ball back and forth. In digital communications, the players are computers, and the required coordination involves unpredictably adjusting "live clocks" that step these computers through phases of a cycle. We show how this phasing, which we call logical synchronization, constrains number-carrying networks, and, if a spacetime manifold in invoked, put "stripes" on spacetime. Via its logically synchronized channels, a network of live clocks serves as a reference against which to locate events. Such a network in any case underpins a coordinate frame, and in some cases the direct use of a network can be tailored to investigate an unpredictable environment. Examples include explorations of gravitational variations near Earth.

  7. Robot technology and numbers in the classroom

    DEFF Research Database (Denmark)

    Majgaard, Gunver; Nielsen, Jacob; Misfeldt, Morten

    2010-01-01

    This paper explores how a cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher. The tool is called Speakmath and it com......This paper explores how a cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher. The tool is called Speakmath...... and it combines physical interaction, learning, and immediate feedback. Speakmath supports the children’s understanding of place value in the sense that it allows them to experiment and create large numbers. Surprisingly the children found it very fun to express very large numbers, and also made smalls contests...... about who could build the largest number. This made a close tie between learning goals, game play, and the core of Speakmath....

  8. Seniority Number in Valence Bond Theory.

    Science.gov (United States)

    Chen, Zhenhua; Zhou, Chen; Wu, Wei

    2015-09-08

    In this work, a hierarchy of valence bond (VB) methods based on the concept of seniority number, defined as the number of singly occupied orbitals in a determinant or an orbital configuration, is proposed and applied to the studies of the potential energy curves (PECs) of H8, N2, and C2 molecules. It is found that the seniority-based VB expansion converges more rapidly toward the full configuration interaction (FCI) or complete active space self-consistent field (CASSCF) limit and produces more accurate PECs with smaller nonparallelity errors than its molecular orbital (MO) theory-based analogue. Test results reveal that the nonorthogonal orbital-based VB theory provides a reverse but more efficient way to truncate the complete active Hilbert space by seniority numbers.

  9. Baryon number nonconservation in extreme conditions

    International Nuclear Information System (INIS)

    Matveev, V.A.; Rubakov, V.A.; Tavkhelidze, A.N.; Shaposhnikov, M.E.

    1988-01-01

    In gauge theories with the left-right asymmetric fermionic content (e.g. in standard electroweak theory) fermion number F is not conserved due to the anomaly. It is shown that anomalous processes, while being exponentially suppressed, under normal conditions, are in fact rapid. The mechanism of fermionic number nonconservation connected with a level crossing phenomenon in external gauge fields is described. The theory and experimental consequences of monopole catalysis of a proton decay is reviewed. It is shown that cold dense fermionic matter is stable only up to some limiting density. It is demonstrated that there is no exponential suppression of the rate F nonconservation at high temperatures. The cosmological implications of this fact are discussed. The strong anomalous fermionic number violation in decays of superheavy fermions technibaryons is considered

  10. Congruent numbers with many prime factors.

    Science.gov (United States)

    Tian, Ye

    2012-12-26

    Mohammed Ben Alhocain, in an Arab manuscript of the 10th century, stated that the principal object of the theory of rational right triangles is to find a square that when increased or diminished by a certain number, m becomes a square [Dickson LE (1971) History of the Theory of Numbers (Chelsea, New York), Vol 2, Chap 16]. In modern language, this object is to find a rational point of infinite order on the elliptic curve my2 = x3 - x. Heegner constructed such rational points in the case that m are primes congruent to 5,7 modulo 8 or twice primes congruent to 3 modulo 8 [Monsky P (1990) Math Z 204:45-68]. We extend Heegner's result to integers m with many prime divisors and give a sketch in this report. The full details of all the proofs will be given in ref. 1 [Tian Y (2012) Congruent Numbers and Heegner Points, arXiv:1210.8231].

  11. Room Airflows with Low Reynolds Number Effects

    DEFF Research Database (Denmark)

    Topp, Claus; Nielsen, Peter V.; Davidson, Lars

    is limited. It has been the objective to investigate the behaviour of a plane isothermal wall jet in a full-scale ventilated room at low Reynolds numbers, i.e. when the flow is not fully turbulent. The results are significantly different from known theory for fully turbulent flows. It was found that the jet......The behaviour of room airflows under fully turbulent conditions is well known both in terms of experiments and, numerical calculations by computational fluid dynamics (CFD). For room airflows where turbulence is not fully developed though, i.e. flows at low Reynolds numbers, the existing knowledge...... constants are a strong function of the Reynolds number up to a level of Reh≈500....

  12. Droplet Number Concentration Value-Added Product

    Energy Technology Data Exchange (ETDEWEB)

    Riihimaki, L. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); McFarlane, S. [DOE ARM Climate Research Facility, Washington, DC (United States); Sivaraman, C. [Pacific Northwest National Lab. (PNNL), Richland, WA (United States)

    2014-06-01

    The ndrop_mfrsr value-added product (VAP) provides an estimate of the cloud droplet number concentration of overcast water clouds retrieved from cloud optical depth from the multi-filter rotating shadowband radiometer (MFRSR) instrument and liquid water path (LWP) retrieved from the microwave radiometer (MWR). When cloud layer information is available from vertically pointing lidar and radars in the Active Remote Sensing of Clouds (ARSCL) product, the VAP also provides estimates of the adiabatic LWP and an adiabatic parameter (beta) that indicates how divergent the LWP is from the adiabatic case. quality control (QC) flags (qc_drop_number_conc), an uncertainty estimate (drop_number_conc_toterr), and a cloud layer type flag (cloud_base_type) are useful indicators of the quality and accuracy of any given value of the retrieval. Examples of these major input and output variables are given in sample plots in section 6.0.

  13. Permeable disks at low Reynolds numbers

    Science.gov (United States)

    Viola, Ignazio Maria; Cummins, Cathal; Mastropaolo, Enrico; Nakayama, Naomi

    2017-11-01

    The wake of a permeable disk can be rather exceptional: a toroidal vortex can form and remains stably at a fixed distance from the disk. The streamwise length of the vortex depends on the Reynolds and Darcy numbers. We investigate this fascinating flow for Reynolds numbers from 10 to 130 and Darcy numbers (Da) from 10-9 to 1. Direct numerical simulations are performed on a 2D grid with axisymmetric boundary conditions. Three flow regimes are observed: for low Da (effectively impervious), the wake is characterized by the presence of a toroidal vortex whose length is approximately equal to that of an impervious disk. For 10-6 RPG-2015-255].

  14. Large numbers hypothesis. II - Electromagnetic radiation

    Science.gov (United States)

    Adams, P. J.

    1983-01-01

    This paper develops the theory of electromagnetic radiation in the units covariant formalism incorporating Dirac's large numbers hypothesis (LNH). A direct field-to-particle technique is used to obtain the photon propagation equation which explicitly involves the photon replication rate. This replication rate is fixed uniquely by requiring that the form of a free-photon distribution function be preserved, as required by the 2.7 K cosmic radiation. One finds that with this particular photon replication rate the units covariant formalism developed in Paper I actually predicts that the ratio of photon number to proton number in the universe varies as t to the 1/4, precisely in accord with LNH. The cosmological red-shift law is also derived and it is shown to differ considerably from the standard form of (nu)(R) - const.

  15. Different Brains Process Numbers Differently: Structural Bases of Individual Differences in Spatial and Nonspatial Number Representations

    NARCIS (Netherlands)

    Krause, F.; Lindemann, O.; Toni, I.; Bekkering, H.

    2014-01-01

    A dominant hypothesis on how the brain processes numerical size proposes a spatial representation of numbers as positions on a "mental number line." An alternative hypothesis considers numbers as elements of a generalized representation of sensorimotor-related magnitude, which is not obligatorily

  16. Detection of Chern numbers and entanglement in topological multi-component systems through subsystem winding numbers

    NARCIS (Netherlands)

    J. Lisle, de; De, S.; Alba, E.; Bullivant, A.; Garcia-Ripoll, J.J.; Lahtinen, V.; Pachos, J.K.

    2014-01-01

    Topological invariants, such as the Chern number, characterize topological phases of matter. Here we provide a method to detect Chern numbers in systems with two distinct species of fermion, such as spins, orbitals or several atomic states. We analytically show that the Chern number can be

  17. Quantum walks assisted by particle number fluctuations

    Science.gov (United States)

    Vargas-Hernandez, Rodrigo A.; v Krems, Roman

    2017-04-01

    We consider quantum walks of particles governed by lattice Hamiltonians with particle-number changing interactions. We show that such interactions, even if weak, accelerate quantum walks at short times due to Rabi oscillations between different particle number subspaces. We examine the dynamics of quantum walks governed by Hamiltonians arising in the context of D-wave quantum annealing experiments and experiments with excitations of ultracold molecules in optical lattices. The same Hamiltonians describe excitations in ensembles of highly magnetic atoms, such as Dy.

  18. Robot technology and numbers in the classroom

    DEFF Research Database (Denmark)

    Majgaard, Gunver; Nielsen, Jacob; Misfeldt, Morten

    2010-01-01

    This paper explores how a cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher. The tool is called Speakmath and it com......This paper explores how a cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher. The tool is called Speakmath...

  19. Energy information data base: report number codes

    International Nuclear Information System (INIS)

    1979-09-01

    Each report processed by the US DOE Technical Information Center is identified by a unique report number consisting of a code plus a sequential number. In most cases, the code identifies the originating installation. In some cases, it identifies a specific program or a type of publication. Listed in this publication are all codes that have been used by DOE in cataloging reports. This compilation consists of two parts. Part I is an alphabetical listing of report codes identified with the issuing installations that have used the codes. Part II is an alphabetical listing of installations identified with codes each has used

  20. Hodge Numbers from Picard-Fuchs Equations

    Science.gov (United States)

    Doran, Charles F.; Harder, Andrew; Thompson, Alan

    2017-06-01

    Given a variation of Hodge structure over P^1 with Hodge numbers (1,1,\\dots,1), we show how to compute the degrees of the Deligne extension of its Hodge bundles, following Eskin-Kontsevich-Möller-Zorich, by using the local exponents of the corresponding Picard-Fuchs equation. This allows us to compute the Hodge numbers of Zucker's Hodge structure on the corresponding parabolic cohomology groups. We also apply this to families of elliptic curves, K3 surfaces and Calabi-Yau threefolds.

  1. Searches for violation of muon number conservation

    International Nuclear Information System (INIS)

    Redwine, R.P.

    1981-01-01

    The question of violation of muon number conservation is one which has occupied considerable attention and resources in recent years. The first generation of experiments at the medium energy accelerators has now been completed and the next generation of experiments is ready to begin. The history of muon number conservation is reviewed, including the reasons for the present belief that the conservation law may not be exact. The experiments that have been completed in the last few years are discussed. The new experiments that are being mounted and planned at several laboratories are discussed, and the relationship of these types of experiments to other studies, such as searches for neutrino oscillations, are considered

  2. The nine numbers of the cosmos

    CERN Document Server

    Rowan-Robinson, Michael

    1999-01-01

    How old is the universe? How far away are the galaxies and how fast are they travelling away from us? What is dark matter and why do astronomers think it pervades the universe? How heavy is the vacuum? How do galaxies form?Michael Rowan-Robinson answers these and many more questions in a highly original and intriguing way. He encapsulates our current knowledge (both what we do and don't know) of the origin and the nature of the universe into nine numbers. These cosmic numbers appear to be independent characteristics of our universe and include its age, the Hubble constant (a measure of its rat

  3. History of the theory of numbers

    CERN Document Server

    Dickson, Leonard Eugene

    2005-01-01

    The three-volume series History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This second volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subject of diophantine analysis. It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms.Featured topics include

  4. Developing Children's Number Sense Using Calculators

    Directory of Open Access Journals (Sweden)

    Hamzah Hamzah

    2016-02-01

    Full Text Available In the past, most people believed that calculators were useful only for obtaining or checking answers to computation problems. Therefore, in many ways they have often been ignored as a teaching resource. Based on the lack of interest, some parents and teachers have shied away from calculator's use, especially in primary mathematics. Many researchers have also found that using calculators as a teaching aid is most useful and effective in developing number sense and mental computation. The Calculator-Aware Number (CAN project in Britain found that children develop their own strategies for carrying out calculations and achieve a high level of numeracy when using calculators

  5. Turbulent pipe flow at extreme Reynolds numbers.

    Science.gov (United States)

    Hultmark, M; Vallikivi, M; Bailey, S C C; Smits, A J

    2012-03-02

    Both the inherent intractability and complex beauty of turbulence reside in its large range of physical and temporal scales. This range of scales is captured by the Reynolds number, which in nature and in many engineering applications can be as large as 10(5)-10(6). Here, we report turbulence measurements over an unprecedented range of Reynolds numbers using a unique combination of a high-pressure air facility and a new nanoscale anemometry probe. The results reveal previously unknown universal scaling behavior for the turbulent velocity fluctuations, which is remarkably similar to the well-known scaling behavior of the mean velocity distribution.

  6. Metric propositional neighborhood logics on natural numbers

    DEFF Research Database (Denmark)

    Bresolin, Davide; Della Monica, Dario; Goranko, Valentin

    2013-01-01

    Metric Propositional Neighborhood Logic (MPNL) over natural numbers. MPNL features two modalities referring, respectively, to an interval that is “met by” the current one and to an interval that “meets” the current one, plus an infinite set of length constraints, regarded as atomic propositions...... is decidable in double exponential time and expressively complete with respect to a well-defined sub-fragment of the two-variable fragment FO2[N,=,numbers. Moreover, we show that MPNL can be extended in a natural way...

  7. Type number and rigidity of fibred surfaces

    International Nuclear Information System (INIS)

    Markov, P E

    2001-01-01

    Infinitesimal l-th order bendings, 1≤l≤∞, of higher-dimensional surfaces are considered in higher-dimensional flat spaces (for l=∞ an infinitesimal bending is assumed to be an analytic bending). In terms of the Allendoerfer type number, criteria are established for the (r,l)-rigidity (in the terminology of Sabitov) of such surfaces. In particular, an (r,l)-infinitesimal analogue is proved of the classical theorem of Allendoerfer on the unbendability of surfaces with type number ≥3 and the class of (r,l)-rigid fibred surfaces is distinguished

  8. Constructing regular graphs with smallest defining number

    OpenAIRE

    Omoomi, Behnaz; Soltankhah, Nasrin

    2008-01-01

    In a given graph $G$, a set $S$ of vertices with an assignment of colors is a {\\sf defining set of the vertex coloring of $G$}, if there exists a unique extension of the colors of $S$ to a $\\Cchi(G)$-coloring of the vertices of $G$. A defining set with minimum cardinality is called a {\\sf smallest defining set} (of vertex coloring) and its cardinality, the {\\sf defining number}, is denoted by $d(G, \\Cchi)$. Let $ d(n, r, \\Cchi = k)$ be the smallest defining number of all $r$-regular $k$-chrom...

  9. Number in Plato’s Philebus

    Directory of Open Access Journals (Sweden)

    Shetnikov, Andrey

    2009-06-01

    Full Text Available The paper concerns the concept of number (arithmos, important for dialectical method of later Plato. It becomes clear that the arithmos in Plato’s dialectics should be understood as a concrete operation, a sort of tekhne, such as counting, enumeration, compilation of a comprehensive and systematic list, etc., rather then the theoretical number of abstract arithmetic. The author analyses a series of grammatical, musical and rhetorical examples, supplied by Plato in the Philebus and other dialogues, and traces the usage of arithmos and similar words in the earlier tradition, particularly, in Homer, Hesiod, the classical tragedy, and Herodotus.

  10. Number sense how the mind creates mathematics

    CERN Document Server

    Dehaene, Stanislas

    2011-01-01

    Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudime

  11. Number theory and the periodicity of matter

    CERN Document Server

    Boeyens, Jan C A

    2008-01-01

    Presents a fully scientific account of the use of the golden ratio and explores the observation that stable nucleides obey a number theory based general lawThe interest in number theory is worldwide and covers the entire spectrum of human knowledge. Those aspects covered here will not be immediately accessible to the general lay readership, but, scientists of all pursuations immediately appreciate the importance of the applications described hereThe well-known interest of engineers, medical practitioners and information technologists in popular scientific matters, should make this an attractive buy for such individuals. Undergraduate students in these disciplines should be equally interested.

  12. A finite particle number approach to physics

    International Nuclear Information System (INIS)

    Noyes, H.P.

    1984-01-01

    Starting from a discrete, self-generating and self-organizing, recursive model and self-consistent interpretive rules the author constructs: the scale constants of physics (3, 10, 137, 1.7x10 38 ); 3+1 Minkowski space with a discrete metric and the algebraic bound ΔepsilonΔtau >= 1; the Einstein-deBroglie relation; algebraic 'double slit' interference; a single time momentum space scattering theory connected to laboratory experience; an approximation to 'wave functions'; 'local' phase severence and hence both distant correlations and separability; baryon number, lepton number, charge and helicity; msub(p)/msub(e); a cosmology not in disagreement with current observations. (Auth.)

  13. Formulation of baryon number violating collisions

    International Nuclear Information System (INIS)

    Funakubo, Koichi; Otsuki, Shoichiro; Takenaga, Kazunori; Toyoda, Fumihiko.

    1992-01-01

    A new formalism based on path-integral expression of time-evolution operator during tunneling is presented. Instead of instanton calculus in the LSZ formalism, a classical bounce solution leading to sphaleron (instanton action) at high (low) energies is adopted as the tunneling configuration. The formalism is applied to O(3) nonlinear sigma model in two dimensions. For the coupling constant g 2 ≅ 0.1, which may be physical in the sense that the number of produced particles ≅ 100, comparable with that of electroweak theory, the baryon number violating cross section is smaller by orders of magnitude than the so-called unitarity bound. (author)

  14. Energy information data base: report number codes

    Energy Technology Data Exchange (ETDEWEB)

    None

    1979-09-01

    Each report processed by the US DOE Technical Information Center is identified by a unique report number consisting of a code plus a sequential number. In most cases, the code identifies the originating installation. In some cases, it identifies a specific program or a type of publication. Listed in this publication are all codes that have been used by DOE in cataloging reports. This compilation consists of two parts. Part I is an alphabetical listing of report codes identified with the issuing installations that have used the codes. Part II is an alphabetical listing of installations identified with codes each has used. (RWR)

  15. Identifying jet quantum numbers event by event

    International Nuclear Information System (INIS)

    Teper, M.J.

    1979-12-01

    A method is proposed to identify the parton that gives rise to any particular jet. The method improves with the number of particles in the jet, and should indicate which of the jets in a three jet event at PETRA is the gluon jet. (author)

  16. Natural occupation numbers: When do they vanish?

    NARCIS (Netherlands)

    Giesbertz, K.J.H.; Van Leeuwen, R.

    The non-vanishing of the natural orbital (NO) occupation numbers of the one-particle density matrix of many-body systems has important consequences for the existence of a density matrix-potential mapping for nonlocal potentials in reduced density matrix functional theory and for the validity of the

  17. Topics in the theory of numbers

    CERN Document Server

    Erdős, Paul

    2003-01-01

    This rather unique book is a guided tour through number theory. While most introductions to number theory provide a systematic and exhaustive treatment of the subject, the authors have chosen instead to illustrate the many varied subjects by associating recent discoveries, interesting methods, and unsolved problems. In particular, we read about combinatorial problems in number theory, a branch of mathematics co-founded and popularized by Paul Erdös. Janos Suranyis vast teaching experience successfully complements Paul Erdös'ability to initiate new directions of research by suggesting new problems and approaches. This book will surely arouse the interest of the student and the teacher alike. Until his death in 1996, Professor Paul Erdös was one of the most prolific mathematicians ever, publishing close to 1,500 papers. While his papers contributed to almost every area of mathematics, his main research interest was in the area of combinatorics, graph theory, and number theory. He is most famous for proposing...

  18. The Relative Phase Asynchronization between Sunspot Numbers ...

    Indian Academy of Sciences (India)

    minimum sunspot activity (Makarov & Makarova 1996), the phase relation between ... evolve in phase. To account for this possibility, we study the phase relation between occurrence of polar faculae and sunspot numbers not only for the total ..... The authors thank the anonymous referee for her/his careful reading of the.

  19. Bernoulli Numbers and the Riemann Zeta Function

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 8; Issue 7. Bernoulli Numbers and the Riemann Zeta Function. B Sury. General Article Volume 8 Issue 7 July 2003 pp 54-62. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/008/07/0054-0062. Keywords.

  20. Some Functional Equations Originating from Number Theory

    Indian Academy of Sciences (India)

    We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.

  1. Preferential solvation: dividing surface vs excess numbers.

    Science.gov (United States)

    Shimizu, Seishi; Matubayasi, Nobuyuki

    2014-04-10

    How do osmolytes affect the conformation and configuration of supramolecular assembly, such as ion channel opening and actin polymerization? The key to the answer lies in the excess solvation numbers of water and osmolyte molecules; these numbers are determinable solely from experimental data, as guaranteed by the phase rule, as we show through the exact solution theory of Kirkwood and Buff (KB). The osmotic stress technique (OST), in contrast, purposes to yield alternative hydration numbers through the use of the dividing surface borrowed from the adsorption theory. However, we show (i) OST is equivalent, when it becomes exact, to the crowding effect in which the osmolyte exclusion dominates over hydration; (ii) crowding is not the universal driving force of the osmolyte effect (e.g., actin polymerization); (iii) the dividing surface for solvation is useful only for crowding, unlike in the adsorption theory which necessitates its use due to the phase rule. KB thus clarifies the true meaning and limitations of the older perspectives on preferential solvation (such as solvent binding models, crowding, and OST), and enables excess number determination without any further assumptions.

  2. Some functional equations originating from number theory

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations. Keywords. Functional equation; stability; multiplicative function. 1. Introduction. In 1940, Ulam gave a wide ranging talk before the Mathematics ...

  3. Contributions to Analytic Number Theory | Lucht | Quaestiones ...

    African Journals Online (AJOL)

    This paper reports on some recent contributions to the theory of multiplicative arithmetic semigroups, which have been initiated by John Knopfmacher's work on analytic number theory. They concern weighted inversion theorems of the. Wiener type, mean-value theorems for multiplicative functions, and, Ramanujan

  4. A Geometrical Application of Number Theory

    Science.gov (United States)

    Srinivasan, V. K.

    2013-01-01

    Any quadruple of natural numbers {a, b, c, d} is called a "Pythagorean quadruple" if it satisfies the relationship "a[superscript 2] + b[superscript 2] + c[superscript 2]". This "Pythagorean quadruple" can always be identified with a rectangular box of dimensions "a greater than 0," "b greater than…

  5. p-adic numbers in physics

    International Nuclear Information System (INIS)

    Brekke, L.; Freund, P.G.O.

    1993-01-01

    The boundary of the ordinary open string world sheet is the real line. Along with the usual open string, one can consider p-adic open strings whose world sheet has as boundary the p-adic line instead (the points on this boundary are labelled by p-adic numbers rather than real numbers). The world sheet itself is then no longer a continuous manifold but becomes a discrete homogeneous Bethe lattice, or Bruhat-Tits tree of incidence number p + 1. The p-adic strings thus correspond to specific discretizations of the world sheet. Studying all these discretizations (one for each prime p) together, as suggested by number theory, sheds new light on the ordinary string, via adelic product formulae. One is also led this way to a new type of string, the adelic string. These issues and their generalization to closed strings are discussed after a self-contained mathematical introduction. Other physical systems with natural p-adic counterparts are considered and in their context the connection between p-adic theories and quantum groups is explored. (orig.)

  6. Some functional equations originating from number theory

    Indian Academy of Sciences (India)

    We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, and investigate the solutions of the equations. Moreover, we will also study some stability problems of those equations.

  7. Morphology and chromosome numbers of Gongronema latifolia ...

    African Journals Online (AJOL)

    Cytological studies on the root-tips of four clones of Gongronema latifolia Benth. were conducted to identify cross-compatible clones for possible improvement through hybridisation. The results showed that the diploid chromosomes number in G. latifolia was 2n = 16. Clones, IMS-20-NJIABA, AKS-33-EKPENE EDIENE, ...

  8. Some inequalities for the Bell numbers

    Indian Academy of Sciences (India)

    Feng Qi

    2017-08-19

    Aug 19, 2017 ... 551. Some inequalities for the Bell numbers. FENG QI1,2,3,∗. 1Institute of Mathematics, Henan Polytechnic University, Jiaozuo City 454010, Henan. Province, China. 2College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City. 028043, Inner Mongolia Autonomous Region, China.

  9. Sustaining Student Numbers in the Competitive Marketplace

    Science.gov (United States)

    Szekeres, Judy

    2010-01-01

    The climate of competition for students in the higher education sector makes it imperative that institutions increase their marketing efforts, both domestically and internationally, to help sustain student numbers. In Australia, the Bradley Report and the government response, which will do away with quotas, allows for a much freer market than…

  10. Some functional equations originating from number theory

    Indian Academy of Sciences (India)

    R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

    Department of Mathematics, Chungnam National University, 305-764 Daejon, Korea. E-mail: smjung@wow.hongik.ac.kr; jhbae@math.cnu.ac.kr. MS received 15 September 2002. Abstract. We will introduce new functional equations (3) and (4) which are strongly related to well-known formulae (1) and (2) of number theory, ...

  11. MORPHOLOGY AND CHROMOSOME NUMBERS OF Gongronema ...

    African Journals Online (AJOL)

    journal

    Cytological studies on the root-tips of four clones of Gongronema latifolia Benth. were conducted to identify cross-compatible clones for possible improvement through hybridisation. The results showed that the diploid chromosomes number in G. latifolia was 2n = 16. Clones, IMS-20-NJIABA, AKS-33-EKPENE EDIENE, ANS-.

  12. The Learning Potentials of Number Blocks

    DEFF Research Database (Denmark)

    Majgaard, Gunver; Nielsen, Jacob; Misfeldt, Morten

    2012-01-01

    This paper describes an initial exploration of how an interactive cubic user-configurable modular robotic system can be used to support learning about numbers and how they are pronounced. The development is done in collaboration with a class of 7-8 year old children and their mathematics teacher...

  13. The number of expats is rather stable

    DEFF Research Database (Denmark)

    Andersen, Torben

    2008-01-01

    aggregate data from the Danish economist’s and the engineer’s trade unions show that during the last decade there has been stagnation in the number of expatriates. Taking into consideration that the three trade unions cover the very large majority of Danish knowledge workers occupying foreign job...

  14. Fractional fermion number and its thermal effect

    International Nuclear Information System (INIS)

    Midorikawa, Shoichi.

    1984-06-01

    We give the general method to calculate fermion numbers induced on solitons in quantum field theory. Our method preserves the symmetry of the Lagrangian. We also extend our analysis to the case of finite temperatures, where we compare our analysis with others. (author)

  15. Visualizing the Arithmetic of Complex Numbers

    Science.gov (United States)

    Soto-Johnson, Hortensia

    2014-01-01

    The Common Core State Standards Initiative stresses the importance of developing a geometric and algebraic understanding of complex numbers in their different forms (i.e., Cartesian, polar and exponential). Unfortunately, most high school textbooks do not offer such explanations much less exercises that encourage students to bridge geometric and…

  16. Reproduction numbers of infectious disease models

    Directory of Open Access Journals (Sweden)

    Pauline van den Driessche

    2017-08-01

    Full Text Available This primer article focuses on the basic reproduction number, ℛ0, for infectious diseases, and other reproduction numbers related to ℛ0 that are useful in guiding control strategies. Beginning with a simple population model, the concept is developed for a threshold value of ℛ0 determining whether or not the disease dies out. The next generation matrix method of calculating ℛ0 in a compartmental model is described and illustrated. To address control strategies, type and target reproduction numbers are defined, as well as sensitivity and elasticity indices. These theoretical ideas are then applied to models that are formulated for West Nile virus in birds (a vector-borne disease, cholera in humans (a disease with two transmission pathways, anthrax in animals (a disease that can be spread by dead carcasses and spores, and Zika in humans (spread by mosquitoes and sexual contacts. Some parameter values from literature data are used to illustrate the results. Finally, references for other ways to calculate ℛ0 are given. These are useful for more complicated models that, for example, take account of variations in environmental fluctuation or stochasticity. Keywords: Basic reproduction number, Disease control, West Nile virus, Cholera, Anthrax, Zika virus

  17. Hurdles in Acquiring the Number Word Sequence

    Science.gov (United States)

    Gould, Peter

    2016-01-01

    Learning the sequence of number words in English up to 30 is not a simple process. In NSW government schools taking part in "Early Action for Success," over 800 students in each of the first 3 years of school were assessed every 5 weeks over the school year to determine the highest correct oral count they could produce. Rather than…

  18. How Can Syntax Support Number Word Acquisition?

    Science.gov (United States)

    Syrett, Kristen; Musolino, Julien; Gelman, Rochel

    2012-01-01

    We expand upon a previous proposal by Bloom and Wynn (1997) that young children learn about the meaning of number words by tracking their occurrence in particular syntactic environments, in combination with the discourse context in which they are used. An analysis of the Childes database (MacWhinney, 2000) reveals that the environments studied by…

  19. Chinese Number Words, Culture, and Mathematics Learning

    Science.gov (United States)

    Ng, Sharon Sui Ngan; Rao, Nirmala

    2010-01-01

    This review evaluates the role of language--specifically, the Chinese-based system of number words and the simplicity of Chinese mathematical terms--in explaining the relatively superior performance of Chinese and other East Asian students in cross-national studies of mathematics achievement. Relevant research is critically reviewed focusing on…

  20. Atmospheric ultrafine aerosol number concentration and its ...

    Indian Academy of Sciences (India)

    may be due to the development of warm thermal layer on valley floor while a cold layer develops along snowy hilltops in winter leading to convection ..... and cut sizes performance for silver, ammonium sulphate and sodium chloride by ... surement and direct display of the number of par- ticles per unit volume of the sampled ...

  1. Radical Software. Number Two. The Electromagnetic Spectrum.

    Science.gov (United States)

    Korot, Beryl, Ed.; Gershuny, Phyllis, Ed.

    1970-01-01

    In an effort to foster the innovative uses of television technology, this tabloid format periodical details social, educational, and artistic experiments with television and lists a large number of experimental videotapes available from various television-centered groups and individuals. The principal areas explored in this issue include cable…

  2. The New Element Curium (Atomic Number 96)

    Science.gov (United States)

    Seaborg, G. T.; James, R. A.; Ghiorso, A.

    1948-01-01

    Two isotopes of the element with atomic number 96 have been produced by the helium-ion bombardment of plutonium. The name curium, symbol Cm, is proposed for element 96. The chemical experiments indicate that the most stable oxidation state of curium is the III state.

  3. New feature for an old large number

    International Nuclear Information System (INIS)

    Novello, M.; Oliveira, L.R.A.

    1986-01-01

    A new context for the appearance of the Eddington number (10 39 ), which is due to the examination of elastic scattering of scalar particles (ΠK → ΠK) non-minimally coupled to gravity, is presented. (author) [pt

  4. Poison control center - Emergency number (image)

    Science.gov (United States)

    For a poison emergency call 1-800-222-1222 anywhere in the United States. This national hotline number will let you ... is a free and confidential service. All local poison control centers in the U.S. use this national ...

  5. Distribution of squares modulo a composite number

    OpenAIRE

    Aryan, Farzad

    2015-01-01

    In this paper we study the distribution of squares modulo a square-free number $q$. We also look at inverse questions for the large sieve in the distribution aspect and we make improvements on existing results on the distribution of $s$-tuples of reduced residues.

  6. Transfinite Numbers-What is Infinity?

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 3. Transfinite Numbers - What is Infinity? S M Srivastava. General Article Volume 2 Issue 3 March 1997 pp 58-68. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/002/03/0058-0068. Author Affiliations.

  7. Dynamic mental number line in simple arithmetic.

    Science.gov (United States)

    Yu, Xiaodan; Liu, Jie; Li, Dawei; Liu, Hang; Cui, Jiaxin; Zhou, Xinlin

    2016-05-01

    Studies have found that spatial-numerical associations could extend to arithmetic. Addition leads to rightward shift in spatial attention while subtraction leads to leftward shift (e.g., Knops et al. 2009; McCrink et al. 2007; Pinhas & Fischer 2008), which is consistent with the hypothesis of static mental number line (MNL) for arithmetic. The current investigation tested the hypothesis of dynamic mental number line which was shaped by the relative magnitudes of two operands in simple arithmetic. Horizontal and vertical electrooculograms (HEOG and VEOG) during simple arithmetic were recorded. Results showed that the direction of eye movements was dependent on the relative magnitudes of two operands. Subtraction was associated with larger rightward eye movements than addition (Experiment 1), and smaller-operand-first addition (e.g., 2+9) was associated with larger rightward eye movement than larger-operand-first addition (e.g., 9+2) only when the difference of two operands was large (Experiment 2). The results suggest that the direction of the mental number line could be dynamic during simple arithmetic, and that the eyes move along the dynamic mental number line to search for solutions.

  8. Chromosome number and cytomorphological characterization of a ...

    African Journals Online (AJOL)

    Chromosome counts from natural populations of Abrus pulchellus in Nigeria were carried out. Tetraploid (2n = 44) chromosome number was constant in all the samples investigated. The 44 chromosomes fall into three cytomorphological categories: eight metacentric and eight submetacentric pairs, and six acrocentric pairs.

  9. Learning Random Numbers: A Matlab Anomaly

    Czech Academy of Sciences Publication Activity Database

    Savický, Petr; Robnik-Šikonja, M.

    2008-01-01

    Roč. 22, č. 3 (2008), s. 254-265 ISSN 0883-9514 R&D Projects: GA AV ČR 1ET100300517 Institutional research plan: CEZ:AV0Z10300504 Keywords : random number s * machine learning * classification * attribute evaluation * regression Subject RIV: BA - General Mathematics Impact factor: 0.795, year: 2008

  10. A Course in Number Theory and Cryptology

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 6. A Course in Number Theory and Cryptology. Rajat Tandon. Book Review Volume 6 Issue 6 June 2001 pp 91-94. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/006/06/0091-0094 ...

  11. The 17 GHz active region number

    Energy Technology Data Exchange (ETDEWEB)

    Selhorst, C. L.; Pacini, A. A. [IP and D-Universidade do Vale do Paraíba-UNIVAP, São José dos Campos (Brazil); Costa, J. E. R. [CEA, Instituto Nacional de Pesquisas Espaciais, São José dos Campos (Brazil); Giménez de Castro, C. G.; Valio, A. [CRAAM, Universidade Presbiteriana Mackenzie, São Paulo (Brazil); Shibasaki, K., E-mail: caius@univap.br [Nobeyama Solar Radio Observatory/NAOJ, Minamisaku, Nagano 384-1305 (Japan)

    2014-08-01

    We report the statistics of the number of active regions (NAR) observed at 17 GHz with the Nobeyama Radioheliograph between 1992, near the maximum of cycle 22, and 2013, which also includes the maximum of cycle 24, and we compare with other activity indexes. We find that NAR minima are shorter than those of the sunspot number (SSN) and radio flux at 10.7 cm (F10.7). This shorter NAR minima could reflect the presence of active regions generated by faint magnetic fields or spotless regions, which were a considerable fraction of the counted active regions. The ratio between the solar radio indexes F10.7/NAR shows a similar reduction during the two minima analyzed, which contrasts with the increase of the ratio of both radio indexes in relation to the SSN during the minimum of cycle 23-24. These results indicate that the radio indexes are more sensitive to weaker magnetic fields than those necessary to form sunspots, of the order of 1500 G. The analysis of the monthly averages of the active region brightness temperatures shows that its long-term variation mimics the solar cycle; however, due to the gyro-resonance emission, a great number of intense spikes are observed in the maximum temperature study. The decrease in the number of these spikes is also evident during the current cycle 24, a consequence of the sunspot magnetic field weakening in the last few years.

  12. The Relative Phase Asynchronization between Sunspot Numbers ...

    Indian Academy of Sciences (India)

    Abstract. The monthly sunspot numbers compiled by Temmer et al. and the monthly polar faculae from observations of the National Astro- nomical Observatory of Japan, for the interval of March 1954 to March. 1996, are used to investigate the phase relationship between polar faculae and sunspot activity for total solar disk ...

  13. DECREASE IN NUMBERS OF THE EASTERN ROCKHOPPER ...

    African Journals Online (AJOL)

    The number of eastern rockhopper penguins Eudyptes chrysocome filholi breeding at subantarctic Marion Island decreased from about 173 000 pairs in 1994/95 to about 67 000 pairs in 2001/02. During 1994/95–2002/03 pairs fledged on average 0.40 chicks per year, an amount thought insufficient to balance mortality of ...

  14. IEEE Standard for Floating Point Numbers

    Indian Academy of Sciences (India)

    Home; Journals; Resonance – Journal of Science Education; Volume 21; Issue 1. IEEE Standard for Floating Point Numbers. V Rajaraman. General Article Volume 21 Issue 1 January 2016 pp 11-30. Fulltext. Click here to view fulltext PDF. Permanent link: http://www.ias.ac.in/article/fulltext/reso/021/01/0011-0030. Keywords.

  15. The Relative Phase Asynchronization between Sunspot Numbers ...

    Indian Academy of Sciences (India)

    2016-01-27

    Jan 27, 2016 ... The monthly sunspot numbers compiled by Temmer et al. and the monthly polar faculae from observations of the National Astronomical Observatory of Japan, for the interval of March 1954 to March 1996, are used to investigate the phase relationship between polar faculae and sunspot activity for total solar ...

  16. Mirror Numbers and Wigner's ``Unreasonable Effectiveness''

    Science.gov (United States)

    Berezin, Alexander

    2006-04-01

    Wigner's ``unreasonable effectiveness of mathematics in physics'' can be augmented by concept of mirror number (MN). It is defined as digital string infinite in both directions. Example is ()5141327182() where first 5 digits is Pi ``spelled'' backward (``mirrored'') and last 5 digits is the beginning of decimal exp1 string. Let MN be constructed from two different transcendental (or algebraically irrational) numbers, set of such MNs is Cantor-uncountable. Most MNs have contain any finite digital sequence repeated infinitely many times. In spirit of ``Contact'' (C.Sagan) each normal MN contains ``Library of Babel'' of all possible texts and patterns (J.L.Borges). Infinite at both ends, MN do not have any numerical values and, contrary to numbers written in positional systems, all digits in MNs have equal weight -- sort of ``numerological democracy''. In Pythagorean-Platonic models (space-time and physical world originating from pure numbers) idea of MN resolves paradox of ``beginning'' (or ``end'') of time. Because in MNs all digits have equal status, (quantum) randomness leads to more uniform and fully ergodic phase trajectories (cf. F.Dyson, Infinite in All Directions) .

  17. Quantum abacus for counting and factorizing numbers

    Science.gov (United States)

    Suslov, M. V.; Lesovik, G. B.; Blatter, G.

    2011-05-01

    We generalize the binary quantum counting algorithm of Lesovik, Suslov, and Blatter [Phys. Rev. APLRAAN1050-294710.1103/PhysRevA.82.012316 82, 012316 (2010)] to higher counting bases. The algorithm makes use of qubits, qutrits, and qudits to count numbers in a base-2, base-3, or base-d representation. In operating the algorithm, the number nnumber n in the base-d representation; the inverse transformation is fully quantum at the level of individual qudits, while a simpler semiclassical version can be used on the level of qudit registers. Combining registers of qubits, qutrits, and qudits, where d is a prime number, with a simpler single-shot measurement allows us to find the powers of 2, 3, and other primes d in the number n. We show that the counting task naturally leads to the shift operation and an algorithm based on the quantum Fourier transformation. We discuss possible implementations of the algorithm using quantum spin-d systems, d-well systems, and their emulation with spin-1/2 or double-well systems. We establish the analogy between our counting algorithm and the phase estimation algorithm and make use of the latter’s performance analysis in stabilizing our scheme. Applications embrace a quantum metrological scheme to measure voltage (an analog to digital converter) and a simple procedure to entangle multiparticle states.

  18. Optokinetic Stimulation Modulates Neglect for the Number Space: Evidence from Mental Number Interval Bisection

    Science.gov (United States)

    Priftis, Konstantinos; Pitteri, Marco; Meneghello, Francesca; Umiltà, Carlo; Zorzi, Marco

    2012-01-01

    Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL), an analogical, visuospatial representation of number magnitude. The MNL is left-to-right oriented in Western cultures, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in the mental bisection of numerical intervals, with a bias toward larger numbers that are relatively to the right on the MNL. In the present study we investigated the effects of optokinetic stimulation (OKS) – a technique inducing visuospatial attention shifts by means of activation of the optokinetic nystagmus – on number interval bisection. One patient with left neglect following right-hemisphere stroke (BG) and four control patients with right-hemisphere damage, but without neglect, performed the number interval bisection task in three conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, and again to the right of the midpoint following rightward OKS. Moreover, the variability of BG’s performance was smaller following both leftward and rightward OKS, suggesting that the attentional bias induced by OKS reduced the “indifference zone” that is thought to underlie the length effect reported in bisection tasks. We argue that shifts of visuospatial attention, induced by OKS, may affect number interval bisection, thereby revealing an interaction between the processing of the perceptual space and the processing of the number space. PMID:22363280

  19. Optokinetic stimulation modulates neglect for the number space: Evidence from mental number interval bisection

    Directory of Open Access Journals (Sweden)

    Konstantinos ePriftis

    2012-02-01

    Full Text Available Behavioral, neuropsychological, and neuroimaging data support the idea that numbers are represented along a mental number line (MNL, an analogical, visuo-spatial representation of number magnitude. The MNL is left-to-right oriented, with small numbers on the left and larger numbers on the right. Left neglect patients are impaired in processing the left side of the MNL and show a rightward deviation in the mental bisection of numerical intervals. In the present study we investigated the effects of optokinetic stimulation (OKS -a technique inducing spatial attention shifts by means of activation of the optokinetic nystagmus- on mental number interval bisection. One patient with left neglect following right hemisphere stroke (BG and four control patients with right hemisphere damage, but without neglect, performed the mental number interval bisection task in three experimental conditions of OKS: static, leftward, and rightward. In the static condition, BG misbisected to the right of the true midpoint. BG misbisected to the left following leftward OKS, but again to the right of the midpoint following rightward OKS. In contrast, the performance of controls was not significantly affected by the direction of OKS. We argue that shifts of visuospatial attention, induced by OKS, may affect the mental number interval bisection, suggesting the presence of an interaction between the processing of number magnitude and the processing of the perceptual space, in patients with neglect for the mental number space.

  20. Finite-particle-number approach to physics

    Energy Technology Data Exchange (ETDEWEB)

    Noyes, H.P.

    1982-10-01

    Starting from a discrete, self-generating and self-organizing, recursive model and self-consistent interpretive rules we construct: the scale constants of physics (3,10,137,1.7x10/sup 38/); 3+1 Minkowski space with a discrete metric and the algebraic bound ..delta.. is an element of ..delta.. tau is greater than or equal to 1; the Einstein-deBroglie relation; algebraic double slit interference; a single-time momentum-space scattering theory connected to laboratory experience; an approximation to wave functions; local phase severance and hence both distant correlations and separability; baryon number, lepton number, charge and helicity; m/sub p//m/sub e/; a cosmology not in disagreement with current observations.

  1. Reynolds numbers in the early Universe

    CERN Document Server

    Giovannini, Massimo

    2012-01-01

    After electron-positron annihilation and prior to photon decoupling the magnetic Reynolds number is approximately twenty orders of magnitude larger than its kinetic counterpart which is, in turn, smaller than one. In this globally neutral system the large-scale inhomogeneities are provided by the spatial fluctuations of the scalar curvature. Owing to the analogy with the description of Markovian conducting fluids in the presence of acoustic fluctuations, the evolution equations of a putative magnetic field are averaged over the large-scale flow determined by curvature perturbations. General lessons are drawn on the typical diffusion scale of magnetic inhomogeneities. It is speculated that Reynolds numbers prior to electron-positron annihilation can be related to the entropy contained in the Hubble volume during the various stages of the evolution of the conducting plasma.

  2. Rational and irrational numbers from unit resistors

    International Nuclear Information System (INIS)

    Kasperski, Maciej; Kłobus, Waldemar

    2014-01-01

    We address the problem of constructing a network of unit resistors such that it enables the retrieval of an arbitrary value of equivalent resistance. In particular, we employ the notion of continued fractions to construct a ladder network by which we can easily obtain any fractional value resistance. In addition, since any irrational number is associated with an infinite continued fraction, we discuss the convergence of the equivalent resistance of an infinite resistive ladder and various aspects concerning the approximations of arbitrary numbers attained by adding additional resistors successively to the network. The presented methods can be easily implemented in an educational laboratory and offer an interesting addition to the topic of Ohm’s law. (paper)

  3. Finite-particle-number approach to physics

    International Nuclear Information System (INIS)

    Noyes, H.P.

    1982-10-01

    Starting from a discrete, self-generating and self-organizing, recursive model and self-consistent interpretive rules we construct: the scale constants of physics (3,10,137,1.7x10 38 ); 3+1 Minkowski space with a discrete metric and the algebraic bound δ is an element of δ tau is greater than or equal to 1; the Einstein-deBroglie relation; algebraic double slit interference; a single-time momentum-space scattering theory connected to laboratory experience; an approximation to wave functions; local phase severance and hence both distant correlations and separability; baryon number, lepton number, charge and helicity; m/sub p//m/sub e/; a cosmology not in disagreement with current observations

  4. Entanglement distillation protocols and number theory

    International Nuclear Information System (INIS)

    Bombin, H.; Martin-Delgado, M.A.

    2005-01-01

    We show that the analysis of entanglement distillation protocols for qudits of arbitrary dimension D benefits from applying basic concepts from number theory, since the set Z D n associated with Bell diagonal states is a module rather than a vector space. We find that a partition of Z D n into divisor classes characterizes the invariant properties of mixed Bell diagonal states under local permutations. We construct a very general class of recursion protocols by means of unitary operations implementing these local permutations. We study these distillation protocols depending on whether we use twirling operations in the intermediate steps or not, and we study them both analytically and numerically with Monte Carlo methods. In the absence of twirling operations, we construct extensions of the quantum privacy algorithms valid for secure communications with qudits of any dimension D. When D is a prime number, we show that distillation protocols are optimal both qualitatively and quantitatively

  5. Bronchogenic cysts with high CT numbers

    Energy Technology Data Exchange (ETDEWEB)

    Okada, Kenji; Hitomi, Shigeki; Miyake, Masayuki (Kansai Electric Power Co., Inc., Osaka (Japan))

    1984-09-01

    Three patients with roentgenographic evidence of smooth, round mediastinal mass were evaluated by computerized tomographic scanning. The density readings from these three lesions were interpreted as equivalent to solid tissues. However, thoracotomy revealed all 3 lesions were thin-walled bronchogenic cysts containing thick viscid fluids. Histological examination of the cystic walls showed no specific findings such as calcium deposits, just showing histology of the bronchial wall. Chemical analysis of the fluids was not carried out in all three cases. The cause of high CT numbers in these cysts was unclear. Diagnostically, a smooth, round mediastinal mass with high CT number in the paravertebral area medical to the head of the rib might be a bronchogenic cyst.

  6. Meteoritic Parent Bodies: Their Number and Identification

    Science.gov (United States)

    Burbine, T. H.; McCoy, T. J.; Meibom, A.; Gladman, B.; Keil, K.

    2002-03-01

    Extensive collection efforts in Antarctica and the Sahara in the past 10 years have greatly increased the number of known meteorites. Groupings of meteorites according to petrologic, mineralogical, bulk- chemical, and isotopic properties suggest the existence of 100-150 distinct parent bodies. Dynamical studies imply that most meteorites have their source bodies in the main belt and not among the near-Earth asteroids. Spectral observations of asteroids are currently the primary way of determining asteroid mineralogies. Linkages between ordinary chondrites and S asteroids, CM chondrites and C-type asteroids, the HEDs and 4 Vesta, and iron meteorites, enstatite chondrites, and M asteroids are discussed. However, it is difficult to conclusively link most asteroids with particular meteorite groups due to the number of asteroids with similar spectral properties and the uncertainties in the optical, chemical, and physical properties of the asteroid regolith.

  7. Optimal number of pigments in photosynthetic complexes

    International Nuclear Information System (INIS)

    Jesenko, Simon; Žnidarič, Marko

    2012-01-01

    We study excitation energy transfer in a simple model of a photosynthetic complex. The model, described by the Lindblad equation, consists of pigments interacting via dipole–dipole interaction. The overlapping of pigments induces an on-site energy disorder, providing a mechanism for blocking the excitation transfer. Based on the average efficiency as well as the robustness of random configurations of pigments, we calculate the optimal number of pigments that should be enclosed in a pigment–protein complex of a given size. The results suggest that a large fraction of pigment configurations are efficient as well as robust if the number of pigments is properly chosen. We compare the optimal results of the model to the structure of pigment–protein complexes as found in nature, finding good agreement. (paper)

  8. Courant Number and Mach Number Insensitive CE/SE Euler Solvers

    Science.gov (United States)

    Chang, Sin-Chung

    2005-01-01

    It has been known that the space-time CE/SE method can be used to obtain ID, 2D, and 3D steady and unsteady flow solutions with Mach numbers ranging from 0.0028 to 10. However, it is also known that a CE/SE solution may become overly dissipative when the Mach number is very small. As an initial attempt to remedy this weakness, new 1D Courant number and Mach number insensitive CE/SE Euler solvers are developed using several key concepts underlying the recent successful development of Courant number insensitive CE/SE schemes. Numerical results indicate that the new solvers are capable of resolving crisply a contact discontinuity embedded in a flow with the maximum Mach number = 0.01.

  9. Baryon number transfer in hadronic interactions

    International Nuclear Information System (INIS)

    Arakelyan, G.H.; Capella, A.; Kaidalov, A.B.; Shabelski, Yu.M.

    2002-01-01

    The process of baryon number transfer due to string junction propagation in rapidity space is analyzed. It has a significant effect on the net baryon production in pp collisions at mid-rapidities and an even larger effect in the forward hemisphere in the cases of πp and γp interactions. The results of numerical calculations in the framework of the quark-gluon string model are in reasonable agreement with the data. (orig.)

  10. Fermion production despite fermion number conservation

    International Nuclear Information System (INIS)

    Bock, W.; Hetrick, J.E.; Smit, J.

    1995-01-01

    Lattice proposals for a nonperturbative formulation of the Standard Model easily lead to a global U(1) symmetry corresponding to exactly conserved fermion number. The absence of an anomaly in the fermion current would then appear to inhibit anomalous processes, such as electroweak baryogenesis in the early universe. One way to circumvent this problem is to formulate the theory such that this U(1) symmetry is explicitly broken. However we argue that in the framework of spectral flow, fermion creation and annihilation still in fact occurs, despite the exact fermion number conservation. The crucial observation is that fermions are excitations relative to the vacuum, at the surface of the Dirac sea. The exact global U(1) symmetry prohibits a state from changing its fermion number during time evolution, however nothing prevents the fermionic ground state from doing so. We illustrate our reasoning with a model in two dimensions which has axial-vector couplings, first using a sharp momentum cutoff, then using the lattice regulator with staggered fermions. The difference in fermion number between the time evolved state and the ground state is indeed in agreement with the anomaly. Both the sharp momentum cutoff and the lattice regulator break gauge invariance. In the case of the lattice model a mass counterterm for the gauge field is sufficient to restore gauge invariance in the perturbative regime. A study of the vacuum energy shows however that the perturbative counterterm is insufficient in a nonperturbative setting and that further quartic counterterms are needed. For reference we also study a closely related model with vector couplings, the Schwinger model, and we examine the emergence of the θ-vacuum structure of both theories. ((orig.))

  11. Translations on North Korea, Number 552

    Science.gov (United States)

    1977-09-19

    economy, including water for irrigation, electric power, industrial use, drinking, river transporta- tion, fresh water fish propagation, rafting...Pyongyang Art Troupe of our country arrived in Zanzibar on 23 August. The national flags of our country and Tanzania were flying on the flagpoles at...and chairman of the Zanzibar Revolutionary Council, 39 other leading officials of the party and government of Zanzibar and a large number of

  12. The crossing number of composite knots

    OpenAIRE

    Lackenby, Marc

    2008-01-01

    It is a very old conjecture that the crossing number of knots is additive under connected sum. In other words, if K#K' is the connected sum of knots K and K', then does the equality c(K#K') = c(K) + c(K') hold? We prove that c(K#K') is at most c(K) + c(K') and at least (c(K) + c(K'))/152.

  13. Forcing clique immersions through chromatic number

    OpenAIRE

    Gauthier, Gregory; Le, Tien-Nam; Wollan, Paul

    2017-01-01

    Building on recent work of Dvo\\v{r}\\'ak and Yepremyan, we show that every simple graph of minimum degree $7t+7$ contains $K_t$ as an immersion and that every graph with chromatic number at least $3.54t + 4$ contains $K_t$ as an immersion. We also show that every graph on $n$ vertices with no stable set of size three contains $K_{2\\lfloor n/5 \\rfloor}$ as an immersion.

  14. Laser interrogation of latent vehicle registration number

    Energy Technology Data Exchange (ETDEWEB)

    Russo, R.E. [Lawrence Berkeley Lab., CA (United States). Energy and Environment Div.]|[Lawrence Livermore National Lab., CA (United States). Forensic Science Center; Pelkey, G.E. [City of Livermore Police Dept., CA (United States); Grant, P.; Whipple, R.E.; Andresen, B.D. [Lawrence Livermore National Lab., CA (United States). Forensic Science Center

    1994-09-01

    A recent investigation involved automobile registration numbers as important evidentiary specimens. In California, as in most states, small, thin metallic decals are issued to owners of vehicles each year as the registration is renewed. The decals are applied directly to the license plate of the vehicle and typically on top of the previous year`s expired decal. To afford some degree of security, the individual registration decals have been designed to tear easily; they cannot be separated from each other, but can be carefully removed intact from the metal license plate by using a razor blade. In September 1993, the City of Livermore Police Department obtained a blue 1993 California decal that had been placed over an orange 1992 decal. The two decals were being investigated as possible evidence in a case involving vehicle registration fraud. To confirm the suspicion and implicate a suspect, the department needed to known the registration number on the bottom (completely covered) 1992 decal. The authors attempted to use intense and directed light to interrogate the colored stickers. Optical illumination using a filtered white-light source partially identified the latent number. However, the most successful technique used a tunable dye laser pumped by a pulsed Nd:YAG laser. By selectively tuning the wavelength and intensity of the dye laser, backlit illumination of the decals permitted visualization of the underlying registration number through the surface of the top sticker. With optimally-tuned wavelength and intensity, 100% accuracy was obtained in identifying the sequence of latent characters. The advantage of optical techniques is their completely nondestructive nature, thus preserving the evidence for further interrogation or courtroom presentation.

  15. Computational foundations of the visual number sense.

    Science.gov (United States)

    Stoianov, Ivilin Peev; Zorzi, Marco

    2017-01-01

    We provide an emergentist perspective on the computational mechanism underlying numerosity perception, its development, and the role of inhibition, based on our deep neural network model. We argue that the influence of continuous visual properties does not challenge the notion of number sense, but reveals limit conditions for the computation that yields invariance in numerosity perception. Alternative accounts should be formalized in a computational model.

  16. A note on Ramsey numbers for fans

    NARCIS (Netherlands)

    Zhang, Yanbo; Broersma, Haitze J.; Chen, Yaojun

    For two given graphs G1 and G2, the Ramsey number R(G1,G2) is the smallest integer N such that, for any graph G of order N, either G contains G1 as a subgraph or the complement of G contains G2 as a subgraph. A fan Fl is l triangles sharing exactly one vertex. In this note, it is shown that R(Fn,

  17. Pharmacological Regulation of Peroxisome Number in Glia

    Science.gov (United States)

    2008-09-01

    Proliferation The pharmaceutical manipulation of peroxisome number has a long and interesting history. In the 1970s, research was conducted on...montages to illustrate peroxisome morphology. These images were optimally contrasted before collation in Adobe Photoshop . Western blot...point, cells will be transfected with Pex16 fused to a photo -switchable fluorescent protein (Kim et al. 2006). The cells will then be washed out of

  18. From the Editor Vol: 6 number 2

    OpenAIRE

    Ugur Demiray

    2005-01-01

    From the Editor Dear TOJDES Readers Time flies. Another quarter has begun. It is a great pleasure to welcome you to the 18th issue, the Volume: 6, Number: 2 of The Turkish Online Journal of Distance Education (TOJDE), of looking forward. TOJDE has been driving and shaping by our editorial board, reviewers, authors and even unbelievable readers. In the April 2005 issue, TOJDE publishes peer-reviewed distance education articles under four umbrellas: applications, feature topics, researches, ...

  19. European Scientific Notes. Volume 36, Number 2,

    Science.gov (United States)

    1982-02-28

    noted that the alleged Symptom-limited exercise testing is gen- immunity of marathon runners to coronary erally accepted as an integral part of any...marathon runners out of coronary patients. risk, and the motivation pf both physician and Wenger emphasized that there is no fixed dose patient...never 45 ESN 36-2 (1982) RESCUE KITE The accuracy of addition of columns of 2-digit numbers was significantly worse at In emergencies at sea, detection

  20. 431K/CD vehicle number plates

    CERN Multimedia

    GS Department

    2009-01-01

    The Green Plates Service, which is responsible for issuing the 431K/CD vehicle number plates , wishes to apologise for the delay in processing applications over the past weeks. The delay is outside the Service’s control, as it is due to the recent introduction of new rules governing the vehicle registration process in France. Normal service will be resumed as soon as possible. Thank you for your understanding. GS-SEM-LS – Green Plates Service

  1. Prism. Volume 2, Number 1, December 2010

    Science.gov (United States)

    2010-12-01

    As Sunnis in the north saw the destruction and looting taking place in the south as coali- tion troops entered, a number of tribal leaders who had...illegal migration ; human , drug, and small arms trafficking; corruption; endemic and pandemic health problems; poverty; oil bunkering; poaching of...from South America and South Asia to reach Europe and to a lesser extent the United States. In 2007, an estimated 48 metric tons of cocaine valued at

  2. Nowcasting sunshine number using logistic modeling

    Czech Academy of Sciences Publication Activity Database

    Brabec, Marek; Badescu, V.; Paulescu, M.

    2013-01-01

    Roč. 120, č. 1-2 (2013), s. 61-71 ISSN 0177-7971 R&D Projects: GA MŠk LD12009 Grant - others:European Cooperation in Science and Technology(XE) COST ES1002 Institutional research plan: CEZ:AV0Z1030915 Keywords : logistic regression * Markov model * sunshine number Subject RIV: BB - Applied Statistics, Operational Research Impact factor: 1.245, year: 2013

  3. European Scientific Notes. Volume 37, Number 7.

    Science.gov (United States)

    1983-07-31

    convection , mechanical The program was written in BASIC lan- dispersion, and molecular diffusion. guage and is portable, with little The anticipated...during World War II, when the British Naturelle , Paris) explored the connec- government assembled a number of scien- tion between remote sensing and... convected electiica ] smooth sur. ,ne for refe’rence and cali- cags i ilcrc iois h bration. All tet.., were carred out in charges in dielectric lia ’uids

  4. Waving Wing Aerodynamics at Low Reynolds Numbers

    Science.gov (United States)

    2010-07-01

    wing. An attached leading edge vortex has been observed by multiple research groups on both mechanical wing flappers (8; 22; 21; 4) and revolving wing...observed by Ellington et al. (8) in their earlier experiments on the mechanical hawkmoth flapper at Re ≈ 10,000. In these experiments the spanwise flow...on mechanical wing flappers at similar Reynolds numbers, Re ≈ 1,000 and 1,400 respectively. Both sets of experiments revealed a stable attached

  5. Homogeneous nucleation with magic numbers: aluminum.

    Science.gov (United States)

    Girshick, Steven L; Agarwal, Pulkit; Truhlar, Donald G

    2009-10-07

    Homogeneous nucleation of clusters that exhibit magic numbers is studied numerically, using as an example aluminum at 2000 K, based on recent calculations of free energies [Li et al., J. Phys. Chem. C 111, 16227 (2007)] and condensation rate constants [Li and Truhlar, J. Phys. Chem. C 112, 11109 (2008)] that provide a database for Al(i) up to i=60. The nucleation behavior for saturation ratios greater than about 4.5 is found to be dominated by a peak in the free energy change associated with the reaction iAl-->Al(i) at i=55, making it the critical size over a wide range of saturation ratios. Calculated steady-state nucleation rates are many orders of magnitude lower than predicted by classical nucleation theory (CNT). The onset of nucleation is predicted to occur at a saturation ratio of about 13.3, compared to about 5.1 in CNT, while for saturation ratios greater than about 25 the abundance of magic-numbered clusters becomes high enough to invalidate the assumption that cluster growth occurs solely by monomer addition. Transient nucleation is also predicted to be substantially different than predicted by CNT, with a much longer time required to reach steady state: about 10(-4) s at a saturation ratio of 20, compared to about 10(-7) s from CNT. Magic numbers are seen to play an important role in transient nucleation, as the nucleation currents for clusters of adjacent sizes become equal to each other in temporally successive groups, where the largest cluster in each group is the magic-numbered one.

  6. An implementation of the number field sieve

    OpenAIRE

    Elkenbracht-Huizing, Marije

    1996-01-01

    The Number Field Sieve (NFS) is the asymptotically fastest known factoring algorithm for large integers. This article describes an implementation of the NFS, including the choice of two quadratic polynomials, both classical sieving and a special form of lattice sieving (line sieving), the block Lanczos method and a new square root algorithm. Finally some data on factorizations obtained with this implementation are listed, including the record factorization of $12^{151}-1$.

  7. European Scientific Notes. Volume 38, Number 8.

    Science.gov (United States)

    1984-08-01

    group’s Reference existence and its uniqueness with Doise -, W ., and S. Moscovici, eds., Cur- respect to other groups) influences at rent Issues in European...CAET M.A. Howard, USN August 1984 Scientific Director ..... James W . Daniel Volume 38 Editor .................. Larry E. Shaffer Number 8...for shallow- and deep-water research. SCIENCE POuCY 0 Holland’s Science Policy and Budget ..................... .James W . Daniel 438 Organizations

  8. Detecting Prime Numbers via Roots of Polynomials

    Science.gov (United States)

    Dobbs, David E.

    2012-01-01

    It is proved that an integer n [greater than or equal] 2 is a prime (resp., composite) number if and only if there exists exactly one (resp., more than one) nth-degree monic polynomial f with coefficients in Z[subscript n], the ring of integers modulo n, such that each element of Z[subscript n] is a root of f. This classroom note could find use in…

  9. Predicting Social Security numbers from public data

    OpenAIRE

    Acquisti, Alessandro; Gross, Ralph

    2009-01-01

    Information about an individual's place and date of birth can be exploited to predict his or her Social Security number (SSN). Using only publicly available information, we observed a correlation between individuals' SSNs and their birth data and found that for younger cohorts the correlation allows statistical inference of private SSNs. The inferences are made possible by the public availability of the Social Security Administration's Death Master File and the widespread accessibility of per...

  10. Reynolds number effects in combustion noise

    Science.gov (United States)

    Seshan, P. K.

    1981-01-01

    Acoustic emission spectra have been obtained for non-premixed turbulent combustion from two small diameter laboratory gas burners, two commercial gas burners and a large gas burner in the firebox of a Babcock-Wilcox Boiler (50,000 lb steam/hr). The changes in burner size and firing rate represent changes in Reynolds number and changes in air/fuel ratio represent departure from stoichiometric proportions. The combustion efficiency was measured independently through gas analysis. The acoustic spectra obtained from the various burners exhibit a persistent shape over the Reynolds number range of 8200-82,000. The spectra were analyzed for identification of a predictable frequency domain that is most responsive to, and readily correlated with, combustion efficiency. A simple parameter (consisting of the ratio of the average acoustic power output in the most responsive frequency bandwidth to the acoustic power level of the loudest frequency) is proposed whose value increases significantly and unmistakably as combustion efficiency approaches 100%. The dependence of the most responsive frequency domain on the various Reynolds numbers associated with turbulent jets is discussed.

  11. Observer variability in estimating numbers: An experiment

    Science.gov (United States)

    Erwin, R.M.

    1982-01-01

    Census estimates of bird populations provide an essential framework for a host of research and management questions. However, with some exceptions, the reliability of numerical estimates and the factors influencing them have received insufficient attention. Independent of the problems associated with habitat type, weather conditions, cryptic coloration, ete., estimates may vary widely due only to intrinsic differences in observers? abilities to estimate numbers. Lessons learned in the field of perceptual psychology may be usefully applied to 'real world' problems in field ornithology. Based largely on dot discrimination tests in the laboratory, it was found that numerical abundance, density of objects, spatial configuration, color, background, and other variables influence individual accuracy in estimating numbers. The primary purpose of the present experiment was to assess the effects of observer, prior experience, and numerical range on accuracy in estimating numbers of waterfowl from black-and-white photographs. By using photographs of animals rather than black dots, I felt the results could be applied more meaningfully to field situations. Further, reinforcement was provided throughout some experiments to examine the influence of training on accuracy.

  12. Fuel number identification method and device therefor

    International Nuclear Information System (INIS)

    Doi, Takami; Seno, Makoto; Tanaka, Keiji

    1998-01-01

    The present invention provides a method of and a device for automatically identifying the number on the upper surface of a fuel of a fuel assembly in a PWR type reactor. Namely, the number on the upper surface of the fuel assembly of the PWR is not arranged in a row, but indent letters are dispersed to predetermined positions of the surface to be indented. Accordingly, the identification of letters is difficult. In the present invention, the letters are identified by the following procedures. Procedure (1): the letters are detected while having a corner portion of the upper surface of a fuel assembly where the number is indented as characteristic points. A procedure (2): a letter region is determined to a relative position based on the characteristic points while determining indent letters having the same direction as one group. A procedure (3): a letter identification treatment is applied to the letter images in the above-mentioned letter region to identify them. A neural network is used for the letter identification treatment. (N.H.)

  13. Tidal Love Numbers of Neutron Stars

    International Nuclear Information System (INIS)

    Hinderer, Tanja

    2008-01-01

    For a variety of fully relativistic polytropic neutron star models we calculate the star's tidal Love number k 2 . Most realistic equations of state for neutron stars can be approximated as a polytrope with an effective index n ∼ 0.5-1.0. The equilibrium stellar model is obtained by numerical integration of the Tolman-Oppenheimer-Volkhov equations. We calculate the linear l = 2 static perturbations to the Schwarzschild spacetime following the method of Thorne and Campolattaro. Combining the perturbed Einstein equations into a single second-order differential equation for the perturbation to the metric coefficient g tt and matching the exterior solution to the asymptotic expansion of the metric in the star's local asymptotic rest frame gives the Love number. Our results agree well with the Newtonian results in the weak field limit. The fully relativistic values differ from the Newtonian values by up to ∼24%. The Love number is potentially measurable in gravitational wave signals from inspiralling binary neutron stars.

  14. Characterizing overwater roughness Reynolds number during hurricanes

    Science.gov (United States)

    Hsu, S. A.; Shen, Hui; He, Yijun

    2017-11-01

    The Reynolds number, which is the dimensionless ratio of the inertial force to the viscous force, is of great importance in the theory of hydrodynamic stability and the origin of turbulence. To investigate aerodynamically rough flow over a wind sea, pertinent measurements of wind and wave parameters from three data buoys during Hurricanes Kate, Lili, Ivan, Katrina, Rita, and Wilma are analyzed. It is demonstrated that wind seas prevail when the wind speed at 10 m and the wave steepness exceed 9 m s-1 and 0.020, respectively. It is found that using a power law the roughness Reynolds number is statistically significantly related to the significant wave height instead of the wind speed as used in the literature. The reason for this characterization is to avoid any self-correlation between Reynolds number and the wind speed. It is found that although most values of R_{*} were below 500, they could reach to approximately 1000 near the radius of maximum wind. It is shown that, when the significant wave height exceeds approximately 2 m in a wind sea, the air flow over that wind sea is already under the fully rough condition. Further analysis of simultaneous measurements of wind and wave parameters using the logarithmic law indicates that the estimated overwater friction velocity is consistent with other methods including the direct (eddy-covariance flux) measurements, the atmospheric vorticity approach, and the sea-surface current measurements during four slow moving super typhoons with wind speed up to 70 m s-1.

  15. Source-Independent Quantum Random Number Generation

    Science.gov (United States)

    Cao, Zhu; Zhou, Hongyi; Yuan, Xiao; Ma, Xiongfeng

    2016-01-01

    Quantum random number generators can provide genuine randomness by appealing to the fundamental principles of quantum mechanics. In general, a physical generator contains two parts—a randomness source and its readout. The source is essential to the quality of the resulting random numbers; hence, it needs to be carefully calibrated and modeled to achieve information-theoretical provable randomness. However, in practice, the source is a complicated physical system, such as a light source or an atomic ensemble, and any deviations in the real-life implementation from the theoretical model may affect the randomness of the output. To close this gap, we propose a source-independent scheme for quantum random number generation in which output randomness can be certified, even when the source is uncharacterized and untrusted. In our randomness analysis, we make no assumptions about the dimension of the source. For instance, multiphoton emissions are allowed in optical implementations. Our analysis takes into account the finite-key effect with the composable security definition. In the limit of large data size, the length of the input random seed is exponentially small compared to that of the output random bit. In addition, by modifying a quantum key distribution system, we experimentally demonstrate our scheme and achieve a randomness generation rate of over 5 ×103 bit /s .

  16. Psychophysical evidence for the number sense.

    Science.gov (United States)

    Burr, David C; Anobile, Giovanni; Arrighi, Roberto

    2017-02-19

    It is now clear that most animals, including humans, possess an ability to rapidly estimate number. Some have questioned whether this ability arises from dedicated numerosity mechanisms, or is derived indirectly from judgements of density or other attributes. We describe a series of psychophysical experiments, largely using adaptation techniques, which demonstrate clearly the existence of a number sense in humans. The number sense is truly general, extending over space, time and sensory modality, and is closely linked with action. We further show that when multiple cues are present, numerosity emerges as the natural dimension for discrimination. However, when element density increases past a certain level, the elements become too crowded to parse, and the scene is perceived as a texture rather than array of elements. The two different regimes are psychophysically discriminable in that they follow distinct psychophysical laws, and show different dependencies on eccentricity, luminance levels and effects of perceptual grouping. The distinction is important, as the ability to discriminate numerosity, but not texture, correlates with formal maths skills.This article is part of the discussion meeting issue 'The origins of numerical abilities'. © 2017 The Authors.

  17. Psychophysical evidence for the number sense

    Science.gov (United States)

    2018-01-01

    It is now clear that most animals, including humans, possess an ability to rapidly estimate number. Some have questioned whether this ability arises from dedicated numerosity mechanisms, or is derived indirectly from judgements of density or other attributes. We describe a series of psychophysical experiments, largely using adaptation techniques, which demonstrate clearly the existence of a number sense in humans. The number sense is truly general, extending over space, time and sensory modality, and is closely linked with action. We further show that when multiple cues are present, numerosity emerges as the natural dimension for discrimination. However, when element density increases past a certain level, the elements become too crowded to parse, and the scene is perceived as a texture rather than array of elements. The two different regimes are psychophysically discriminable in that they follow distinct psychophysical laws, and show different dependencies on eccentricity, luminance levels and effects of perceptual grouping. The distinction is important, as the ability to discriminate numerosity, but not texture, correlates with formal maths skills. This article is part of the discussion meeting issue ‘The origins of numerical abilities’. PMID:29292350

  18. Identification of copy number variants in horses

    KAUST Repository

    Doan, R.

    2012-03-01

    Copy number variants (CNVs) represent a substantial source of genetic variation in mammals. However, the occurrence of CNVs in horses and their subsequent impact on phenotypic variation is unknown. We performed a study to identify CNVs in 16 horses representing 15 distinct breeds (Equus caballus) and an individual gray donkey (Equus asinus) using a whole-exome tiling array and the array comparative genomic hybridization methodology. We identified 2368 CNVs ranging in size from 197 bp to 3.5 Mb. Merging identical CNVs from each animal yielded 775 CNV regions (CNVRs), involving 1707 protein- and RNA-coding genes. The number of CNVs per animal ranged from 55 to 347, with median and mean sizes of CNVs of 5.3 kb and 99.4 kb, respectively. Approximately 6% of the genes investigated were affected by a CNV. Biological process enrichment analysis indicated CNVs primarily affected genes involved in sensory perception, signal transduction, and metabolism. CNVs also were identified in genes regulating blood group antigens, coat color, fecundity, lactation, keratin formation, neuronal homeostasis, and height in other species. Collectively, these data are the first report of copy number variation in horses and suggest that CNVs are common in the horse genome and may modulate biological processes underlying different traits observed among horses and horse breeds.

  19. Foundations of analysis over surreal number fields

    CERN Document Server

    Alling, NL

    1987-01-01

    In this volume, a tower of surreal number fields is defined, each being a real-closed field having a canonical formal power series structure and many other higher order properties. Formal versions of such theorems as the Implicit Function Theorem hold over such fields. The Main Theorem states that every formal power series in a finite number of variables over a surreal field has a positive radius of hyper-convergence within which it may be evaluated. Analytic functions of several surreal and surcomplex variables can then be defined and studied. Some first results in the one variable case are derived. A primer on Conway''s field of surreal numbers is also given. Throughout the manuscript, great efforts have been made to make the volume fairly self-contained. Much exposition is given. Many references are cited. While experts may want to turn quickly to new results, students should be able to find the explanation of many elementary points of interest. On the other hand, many new results are given, and much mathe...

  20. Comparison of the Variations of Sunspot Number, Number of Sunspot Groups, and Sunspot Area, 1875 -2013

    Science.gov (United States)

    Wilson, Robert M.

    2014-01-01

    Examined are the yearly variations and ratios of sunspot number, the number of sunspot groups, and the total corrected sunspot area for the interval 1875-2013. While yearly sunspot number independently correlates strongly (r = 0.98) with the yearly number of sunspot groups (y = -2 + 11.99x) and the total corrected sunspot area (y = 5 + 0.059x), the strongest correlation (Ry12 = 0.99) is the one based on the bivariate fit of sunspot number against the combined variations of the number of sunspot groups and sunspot area (y = 1 + 5.88x1 + 0.031x2, where y refers to sunspot number, x1 refers to the number of sunspot groups, and x2 refers to the sunspot area). While all cycle minima based on the bivariate fit are concurrent with the observed minimum in sunspot number, cycle maxima are sometimes found to differ. For sunspot cycles 12, 19, 20, and 23, cycle maximum is inferred to have occurred in 1884, 1958, 1970, and 2002, respectively, rather than in 1883, 1957, 1968, and 2000, based on the observed sunspot number. Also, cycle 19's maximum amplitude based on observed sunspot number seems too high in comparison to that found using the bivariate fit. During the 139-year interval 1875-2013, the difference between the observed and predicted sunspot number based on the bivariate fit is sunspot cycle 24, the difference between observed and predicted values has been only -0.7 and 3.2 (=0.5 se).

  1. On the Relation Between Grammatical Number and Cardinal Numbers in Development

    Directory of Open Access Journals (Sweden)

    Barbara W Sarnecka

    2014-10-01

    Full Text Available This mini-review focuses on the question of how the grammatical number system of a child’s language may help the child learn the meanings of cardinal number words (e.g., ‘one’ and ‘two’. Evidence from young children learning English, Russian, Japanese, Mandarin, Slovenian or Saudi Arabic suggests that trajectories of number-word learning differ for children learning different languages. Children learning English, which distinguishes between singular and plural, seem to learn the meaning of the cardinal number ‘one’ earlier than children learning Japanese or Mandarin, which have very little singular/plural marking. Similarly, children whose languages have a singular/dual/plural system (Slovenian and Saudi Arabic learn the meaning of ‘two’ earlier than English-speaking children. This relation between grammatical and cardinal number may shed light on how humans acquire cardinal-number concepts. There is an ongoing debate about whether mental symbols for small cardinalities (concepts for ‘oneness,’ ‘twoness,’ etc. are innate or learned. Although an effect of grammatical number on number-word learning does not rule out nativist accounts, it seems more consistent with constructivist accounts, which portray the number-learning process as one that requires significant conceptual change.

  2. Quantum random-number generator based on a photon-number-resolving detector

    International Nuclear Information System (INIS)

    Ren Min; Wu, E; Liang Yan; Jian Yi; Wu Guang; Zeng Heping

    2011-01-01

    We demonstrated a high-efficiency quantum random number generator which takes inherent advantage of the photon number distribution randomness of a coherent light source. This scheme was realized by comparing the photon flux of consecutive pulses with a photon number resolving detector. The random bit generation rate could reach 2.4 MHz with a system clock of 6.0 MHz, corresponding to a random bit generation efficiency as high as 40%. The random number files passed all the stringent statistical tests.

  3. Small numbers are sensed directly, high numbers constructed from size and density.

    Science.gov (United States)

    Zimmermann, Eckart

    2018-04-01

    Two theories compete to explain how we estimate the numerosity of visual object sets. The first suggests that the apparent numerosity is derived from an analysis of more low-level features like size and density of the set. The second theory suggests that numbers are sensed directly. Consistent with the latter claim is the existence of neurons in parietal cortex which are specialized for processing the numerosity of elements in the visual scene. However, recent evidence suggests that only low numbers can be sensed directly whereas the perception of high numbers is supported by the analysis of low-level features. Processing of low and high numbers, being located at different levels of the neural hierarchy should involve different receptive field sizes. Here, I tested this idea with visual adaptation. I measured the spatial spread of number adaptation for low and high numerosities. A focused adaptation spread of high numerosities suggested the involvement of early neural levels where receptive fields are comparably small and the broad spread for low numerosities was consistent with processing of number neurons which have larger receptive fields. These results provide evidence for the claim that different mechanism exist generating the perception of visual numerosity. Whereas low numbers are sensed directly as a primary visual attribute, the estimation of high numbers however likely depends on the area size over which the objects are spread. Copyright © 2017 Elsevier B.V. All rights reserved.

  4. 17 CFR 232.309 - Paper size; binding; sequential numbering; number of copies.

    Science.gov (United States)

    2010-04-01

    ... electronic format documents. (b) An electronic format document, submitted in the manner prescribed by the... AND EXCHANGE COMMISSION REGULATION S-T-GENERAL RULES AND REGULATIONS FOR ELECTRONIC FILINGS Preparation of Electronic Submissions § 232.309 Paper size; binding; sequential numbering; number of copies...

  5. Attaching Meaning to the Number Words: Contributions of the Object Tracking and Approximate Number Systems

    Science.gov (United States)

    vanMarle, Kristy; Chu, Felicia W.; Mou, Yi; Seok, Jin H.; Rouder, Jeffrey; Geary, David C.

    2018-01-01

    Children's understanding of the quantities represented by number words (i.e., cardinality) is a surprisingly protracted but foundational step in their learning of formal mathematics. The development of cardinal knowledge is related to one or two core, inherent systems--the approximate number system (ANS) and the object tracking system (OTS)--but…

  6. 21 CFR 207.35 - Notification of registrant; drug establishment registration number and drug listing number.

    Science.gov (United States)

    2010-04-01

    ... 21 Food and Drugs 4 2010-04-01 2010-04-01 false Notification of registrant; drug establishment registration number and drug listing number. 207.35 Section 207.35 Food and Drugs FOOD AND DRUG ADMINISTRATION... conditions of display to the consumer (for over-the-counter drug products) or to the dispenser (for...

  7. Generation of Random Numbers and Parallel Random Number Streams for Monte Carlo Simulations

    Directory of Open Access Journals (Sweden)

    L. Yu. Barash

    2012-01-01

    Full Text Available Modern methods and libraries for high quality pseudorandom number generation and for generation of parallel random number streams for Monte Carlo simulations are considered. The probability equidistribution property and the parameters when the property holds at dimensions up to logarithm of mesh size are considered for Multiple Recursive Generators.

  8. The number of families of matter

    International Nuclear Information System (INIS)

    Feldman, G.J.; Steinberger, J.

    1991-01-01

    The universe around us consists of three fundamental particles. They are the up quark, the down quark and the electron. Stars, planets, molecules, atoms - and indeed, ourselves - are built from amalgamations of these three entities. They, together with the neutral and possibly massless partner of the electron, the electron neutrino, constitute the first family of matter. Nature, however, is not so simple. It provides two other families that are like the first in every respect except in their mass. Why did nature happen to provide three replications of the same pattern of matter? The authors theories as yet give no indication. Could there be more than three families? Recent experiments have led to the conclusion that there are not. In the spring and summer of 1989, experiments were performed by teams of physicists working at the Sanford Linear Accelerator Center (SLAC) and the European laboratory for particle physics (CERN) near Geneva. The teams used machines of differing designs to cause electrons (e - ) and positrons (e + ) to collide and thus produce quantities of the Z particle (or Z degree, pronounced zee zero or zee naught). The most massive elementary particle observed, the Z weighs about 100 times as much as a proton and nearly as much as an atom of silver. As the authors shall see, this mass is merely an average. The Z lifetime is so short that individual Z particles differ slightly in their mass. The spread in the mass values is called a mass width, a quantity that depends on the number of families of matter. Because this width can be measured experimentally, the number of families of matter can be inferred. In this article they describe the experiments by which the families of matter were numbered

  9. Effective atomic number of dental smalt

    International Nuclear Information System (INIS)

    Rodas D, J.E.; Nogueira, M.S.

    1998-01-01

    The effective atomic numbers Z are enough utilized for to characterize the interactions of ionizing radiation with matter. Particularly for the Z calculation in biological tissues and/or composed materials we need to know the relationship between the cross sections of the diverse radiations interactions with mattera and the atomic numbers Z of the constituent elements in the tissue or composed material. Normally the cross section by atom σ 2 is proportional to Z m . The m value depends of the iterative process type and the energy of the incident photons. In the case of the photoelectric interaction, the m vary will vary between 4,698 and 4,799 for energies between 10 to 200 keV. It was verified that constituent elements with high Z (>20) they had a major contribution. The m values for the Compton interation and the coherent scattering were calculated of similar way. Knowing the m values, we calculate the partials Z of a composed material. For the calculation of total Z, we can use alternatives starting from the equivalent atomic number corresponding to the total cross section σ d tot, mc of the composed material. In this work for the calculation of Z values corresponding to diverse interations, we applied a linear regression at the values of Ln σ a x LnZ for different energies. In general, to characterize a simulator material of a tissue or composed material we need to know the total Z in function of the photon energy applied to dental smalt increases until some hundreds of keV the partial values of Z owing to photoelectric effect and the coherent scattering this is owing to the smalt has a great concentration of elements with high Z. (Author)

  10. Elliptic Tales Curves, Counting, and Number Theory

    CERN Document Server

    Ash, Avner

    2012-01-01

    Elliptic Tales describes the latest developments in number theory by looking at one of the most exciting unsolved problems in contemporary mathematics--the Birch and Swinnerton-Dyer Conjecture. The Clay Mathematics Institute is offering a prize of 1 million to anyone who can discover a general solution to the problem. In this book, Avner Ash and Robert Gross guide readers through the mathematics they need to understand this captivating problem. The key to the conjecture lies in elliptic curves, which are cubic equations in two variables. These equations may appear simple, yet they arise from

  11. Betti numbers of powers of ideals

    Directory of Open Access Journals (Sweden)

    Gioia Failla

    2008-11-01

    Full Text Available Let A=K[x1, ..... ,xn] be a standard graded polynomial ring over a field K, let M = (x_1, .... , x_n be the graded maximal ideal and I a graded ideal of A. For each i the Betti numbers b_i(I^k of I^k are polynomial functions for k>>0. We show that if I is M-primary, then these polynomial functions have the same degree for all i .

  12. Baryon number violation via Majorana neutrinos

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Yue [Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125 (United States)

    2016-06-21

    We propose and investigate a novel, minimal, and experimentally testable framework for baryo- genesis, dubbed dexiogenesis, using baryon number violating effective interactions of right-handed Majorana neutrinos responsible for the seesaw mechanism. The distinct LHC signature of our framework is same-sign top quark final states, possibly originating from displaced vertices. The region of parameters relevant for LHC phenomenology can also yield concomitant signals in nucleon decay experiments. We provide a simple ultraviolet origin for our effective operators, by adding a color-triplet scalar, which could ultimately arise from a grand unified theory.

  13. Health Code Number (HCN) Development Procedure

    Energy Technology Data Exchange (ETDEWEB)

    Petrocchi, Rocky; Craig, Douglas K.; Bond, Jayne-Anne; Trott, Donna M.; Yu, Xiao-Ying

    2013-09-01

    This report provides the detailed description of health code numbers (HCNs) and the procedure of how each HCN is assigned. It contains many guidelines and rationales of HCNs. HCNs are used in the chemical mixture methodology (CMM), a method recommended by the department of energy (DOE) for assessing health effects as a result of exposures to airborne aerosols in an emergency. The procedure is a useful tool for proficient HCN code developers. Intense training and quality assurance with qualified HCN developers are required before an individual comprehends the procedure to develop HCNs for DOE.

  14. Getting DNA copy numbers without control samples

    Directory of Open Access Journals (Sweden)

    Ortiz-Estevez Maria

    2012-08-01

    Full Text Available Abstract Background The selection of the reference to scale the data in a copy number analysis has paramount importance to achieve accurate estimates. Usually this reference is generated using control samples included in the study. However, these control samples are not always available and in these cases, an artificial reference must be created. A proper generation of this signal is crucial in terms of both noise and bias. We propose NSA (Normality Search Algorithm, a scaling method that works with and without control samples. It is based on the assumption that genomic regions enriched in SNPs with identical copy numbers in both alleles are likely to be normal. These normal regions are predicted for each sample individually and used to calculate the final reference signal. NSA can be applied to any CN data regardless the microarray technology and preprocessing method. It also finds an optimal weighting of the samples minimizing possible batch effects. Results Five human datasets (a subset of HapMap samples, Glioblastoma Multiforme (GBM, Ovarian, Prostate and Lung Cancer experiments have been analyzed. It is shown that using only tumoral samples, NSA is able to remove the bias in the copy number estimation, to reduce the noise and therefore, to increase the ability to detect copy number aberrations (CNAs. These improvements allow NSA to also detect recurrent aberrations more accurately than other state of the art methods. Conclusions NSA provides a robust and accurate reference for scaling probe signals data to CN values without the need of control samples. It minimizes the problems of bias, noise and batch effects in the estimation of CNs. Therefore, NSA scaling approach helps to better detect recurrent CNAs than current methods. The automatic selection of references makes it useful to perform bulk analysis of many GEO or ArrayExpress experiments without the need of developing a parser to find the normal samples or possible batches within the

  15. Residue number systems theory and applications

    CERN Document Server

    Mohan, P V Ananda

    2016-01-01

    This new and expanded monograph improves upon Mohan's earlier book, Residue Number Systems (Springer, 2002) with a state of the art treatment of the subject. Replete with detailed illustrations and helpful examples, this book covers a host of cutting edge topics such as the core function, the quotient function, new Chinese Remainder theorems, and large integer operations. It also features many significant applications to practical communication systems and cryptography such as FIR filters and elliptic curve cryptography. Starting with a comprehensive introduction to the basics and leading up to current research trends that are not yet widely distributed in other publications, this book will be of interest to both researchers and students alike.

  16. Cancer screening is not only about numbers.

    Science.gov (United States)

    Knottnerus, B J

    2017-05-01

    In the cancer screening debate, arguments for and against screening are often based on statistics, whereas for individuals personal, non-statistical factors are at least as important when deciding whether to participate in screening. Health care professionals have a responsibility in helping individuals navigate in this complex field by identifying and clarifying the individuals' beliefs, fears and preferences while being aware of their own. Moreover, researchers should explore beliefs and motives that matter for individuals and not only report numbers that can be interpreted in different ways. © 2017 John Wiley & Sons Ltd.

  17. The european emergency number 112 - the questionnaire

    OpenAIRE

    Goniewicz Krzysztof; Goniewicz Mariusz; Misztal Okońska Patrycja; Witold Pawłowski; Czerski Robert

    2017-01-01

    Goniewicz Krzysztof, Goniewicz Mariusz, Misztal Okońska Patrycja, Witold Pawłowski, Czerski Robert. The european emergency number 112 - the questionnaire. Journal of Education, Health and Sport. 2017;7(7):1165-1174. eISSN 2391-8306. DOI http://dx.doi.org/10.5281/zenodo.1117736 http://ojs.ukw.edu.pl/index.php/johs/article/view/5134 The journal has had 7 points in Ministry of Science and Higher Education parametric evaluation. Part B item 1223 (26.01....

  18. The Britannica Guide to Numbers and Measurement

    CERN Document Server

    2011-01-01

    The universal language of numbers has allowed individuals to transcend cultural differences and make collaborative efforts to comprehend the world mathematically. Though many of these mathematicians may never have met the predecessors who made their own work possible, their collective works form the foundations of mathematics as it is known today. The books in this series introduce students not only to the theories and formulas that form the basis of each field of mathematics, but to the individuals who dedicated their lives to pushing numerical boundaries. Detailed diagrams provide visual sum

  19. Elementary number theory an algebraic approach

    CERN Document Server

    Bolker, Ethan D

    2007-01-01

    This text uses the concepts usually taught in the first semester of a modern abstract algebra course to illuminate classical number theory: theorems on primitive roots, quadratic Diophantine equations, and the Fermat conjecture for exponents three and four. The text contains abundant numerical examples and a particularly helpful collection of exercises, many of which are small research problems requiring substantial study or outside reading. Some problems call for new proofs for theorems already covered or for inductive explorations and proofs of theorems found in later chapters.Ethan D. Bolke

  20. A Career in Statistics Beyond the Numbers

    CERN Document Server

    Hahn, Gerald J

    2012-01-01

    A valuable guide to a successful career as a statistician A Career in Statistics: Beyond the Numbers prepares readers for careers in statistics by emphasizing essential concepts and practices beyond the technical tools provided in standard courses and texts. This insider's guide from internationally recognized applied statisticians helps readers decide whether a career in statistics is right for them, provides hands-on guidance on how to prepare for such a career, and shows how to succeed on the job. The book provides non-technical guidance for a successful career. The authors' extensive indu